Please type the population mean and population standard deviation, and provide details about the event you want to compute the probability for (for the standard normal distribution, the mean is 0 and the standard . Here, \(2\) and \(8\) are the extremes, while \(5\) and \(4\) are the means. Solution: Since the ratios in the proportion are reciprocated, we can use the second property of proportions. So the point estimate for the proportion is: p ^ = x n = 6 30 = 0.2 = 20 %. The former (a) is called the first or antecedent, and the latter (b) is the second term or consequent.Thus, in the ratio (a:b,\, a) is the antecedent and (b) is the consequent. As a result, understanding the Properties of Proportion is essential. \(a\) and \(b\) could be any two quantities. Once you click away on our proportional relationship calculator and determine two variables that are directly or indirectly proportional to each other in a fraction of seconds. Need some help? When two or more such ratios are equal, they are said to be in proportion. Properties of Proportion A proportion is a situation in which 2 ratios are equal. The fraction form The proportion between a,b and u,v would appear as follows if the fraction layout is used. Subtrahendo If \(a : b = c : d\), then value of each ratio is \(a c : b d\) We can find the missing value by dividing the given values. Proportion is a mathematical comparison between two numbers. When you are solving a proportion, the concept of cross multiplication is applied. Even though the empirical rule is also known as the 68 95 99 rule, it isn't limited to only the percentages of 68%, 95%, and 99.7%. Related Symbolab blog posts. The proportion of the population voting for Mr. Jones is. How to Use a Proportion Calculator? Similarly, if we have two unknown values in a relation, we can use cross . A = 7, B = 13 and C = 6 then D = 11.1428571429, 3. Why Does the Cross Multiplication Calculator for Fractions Work? Using the second property, N = 35. Indirect or inverse proportion, Q.3: What is continued and mean proportion?Ans: Three numbers \(a,\,b,\,c\) are in continued proportion if \(a,b,b,c\) are in proportion.
, If \(p:q = q:r,\) then \(p,\,q,\,r\) are said to be in continued proportion. Solving proportions is a crucial skill when studying similar polygons. As these two ratios are equal, they can be used in the form of proportion. More frequently, the knowledge of ratio and proportion is applied togetherto solveday to day problems. A proportion between two ratios can be expressed using 2 forms. Instructions: This calculator conducts a Chi-Square test for goodness of fit. Therefore, 3 : 4 = 18 : x 3 x = 4 18; from the above property (vi) we know product of extremes = product of means 3x = 72 x = 72/3 Note: exponents must be positive integers, no negatives, decimals, or variables. When we divide two amounts of the same sort, we get a ratio of the two quantities. Is light a wave or a particle? Enter a problem Go! Solve the proportion between 2 fractions and calculate the missing fraction variable inequalities. 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FAQ What Is A Proportion? In other words, we can write the following statement to elaborate on this point. Exponents may not be placed Some of the examples of proportion are: Enter the ratios in the respective input field, Now click the button Solve to get the result, Finally, the true or false for the given proportion will be displayed in the output field. The two terms \(b\) and \(c\) are called \(means\ or\ mean\ terms\), whereas the terms \(a\) and \(d\) are known as extremes or extreme terms., $$\mathbf{\frac{a}{b} = \frac{c}{d} or a:b::c:d$$. 5 goes into 40 eight times. What is cross multiplication? Enter 3 values and 1 unknown. 2) The quantities a, b, c, and d are the "terms" of the proportion. Open the Image Region Analyzer app from the MATLAB toolstrip. In terms of present day algebra, letting the length of the shorter segment be one unit and the length of the longer segment be x units gives rise to the equation ( x + 1)/ x = x /1; this may be rearranged to form the quadratic equation x2 - x - 1 = 0, for which the positive solution is x = (1 + Square root of5 )/2, the golden ratio. There are two basic types of proportion, namely. What is a proportion in a math calculator? document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. Free linear equation calculator - solve linear equations step-by-step Solutions Graphing . For instance, consider that we have the following two ratios which are considered to be equal. The keyword to distinguish proportion in a problem is out of. Thus, the ratio of two numbers (a) and (b\left( {b \ne 0} \right)) is (a \div b) or, (\frac{a}{b}) and is denoted by (a:b. If \(a\) is directly proportional to \(b,\) then it is denoted as \(a \propto b\). 15/2 2/3 = x/6 = 9/y To find the value of y in this proportion you must divide 54 by 4 } },{ "@type": "Question", "name": "How to Solve Proportion Problems with This Calculator? For addition and subtraction, use the standard + and symbols respectively. A proportion between tworatios can be expressed using 2 forms. 4 x 4 = 100 4. .accordion{background-color:#eee;color:#444;cursor:pointer;padding:18px;width:100%;border:none;text-align:left;outline:none;font-size:16px;transition:0.4s}.accordion h3{font-size:16px;text-align:left;outline:none;}.accordion:hover{background-color:#ccc}.accordion h3:after{content:"\002B";color:#777;font-weight:bold;float:right;}.active h3:after{content: "\2212";color:#777;font-weight:bold;float:right;}.panel{padding:0 18px;background-color:white;overflow:hidden;}.hidepanel{max-height:0;transition:max-height 0.2s ease-out}.panel ul li{list-style:disc inside}. Simple Interest Compound Interest . 5. Ratio and Proportion Practice Questions: Properties of Proportion. A ratio is a comparison of two quantities. Free online converters. Random Name Picker - Spin The Wheel to Pick The Winner, Kinematics Calculator - using three different kinematic equations, Quote Search - Search Quotes by Keywords And Authors, Percent Off Calculator - Calculate Percentage, Amortization Calculator - Calculate Loan Payments. If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Proportion Calculator", [online] Available at: https://www.gigacalculator.com/calculators/proportion-calculator.php URL [Accessed Date: 01 Mar, 2023]. This would give you the following equation. For solving proportions problems, we set up the proportions and solve for the missing side length - it will be a variable, or a variable expression Proportion is the statement that identifies the fact that two ratios have equal values. Thus, if \(a,\,b,\,c\) are in continued proportion, then \(a,\,b,\,b,\,c\) are in proportion, i.e., \(a:b::b:c\), \(\Rightarrow \) product of extreme terms \(=\) product of mean terms, If \(a,\,b,\,c\) are in continued proportion, then \(b\) is the mean proportional between \(a\) and \(c.\), If \(b\) is the mean proportional between \(a\) and \(c,\) then \({b^2} = ac.\). Calculate how much 7 pens cost. Great work. The formula for calculating the sample proportion is the number of occurrences ( x) divided by the sample size ( n ): p ^ = x n. In our example, 6 out of 30 were born in the US: x is 6, and n is 30. ## ## proportion power calculation for binomial distribution (arcsine transformation) ## ## h = 0.1318964 ## n = 451.1706 ## sig.level = 0.05 ## power = 0.8 ## alternative = two.sided. on numbers, brackets, or parentheses. Learn more about us. Enter your email address to subscribe to this blog and receive notifications of new posts by email. The value of x in the proportion 1/2:2/3 = 3/4:x is 1 If 2/3 = x/y, then which of the following must be true? The calculator will update "h effect size" field with h effect size (0.11208). Proportion is expressed using the double colon \(\left( {::} \right)\) or adequate to the symbol \(\left( = \right).\) Proportion is an equation. Here, \(2\) and \(64\) are extremes, and \(4\) and \(16\) are means. A = 11, B = 7, C = 29 and D = 18.4545454545 then 11 : 7 = 29 : 18.4545454545 is TRUE. Addition of integers Calculator. What is the proportion of 3 : 5 = x : 40? Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics. In the above sets of ratios, c will be multiplied by q and d will be multiplied by p. In the expression, $m$ equals $12$ and $n$ equals $2$, When multiplying exponents with same base you can add the exponents: $419904yx^{18}y^{24}$, Simplify the fraction $\frac{419904y^{25}x^{18}}{1024x^{2}}$ by $x$. Finance. To solve proportion problems, we use the concept that proportion is two ratios that are equal to each other. Fill in the sample size, n, the number of successes, x, the hypothesized population proportion p 0, and indicate if the test is left tailed, <, right tailed, >, or two tailed, . Dividendo If \(a : b = c : d\), then \(a b : b = c d : d\) Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific Notation Arithmetics. You could use any of the four numbers from the given set of five numbers and set up two equal ratios to form a proportion. In the expression, $m$ equals $4$ and $n$ equals $2$, Simplify $\left(y^2\right)^{4\cdot 2}$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. Introduction to Statistics is our premier online video course that teaches you all of the topics covered in introductory statistics. Then the proportion becomes 1:4 = 1:4. Find out to know how your mom can be instrumental in your score improvement. Thus, 10 4 = x 15. Two quantities are said to be indirectly proportional if on the increase of the one, the other decreases to the same extent and vice-versa. Exponent properties Calculator & Solver - SnapXam Exponent properties Calculator Get detailed solutions to your math problems with our Exponent properties step-by-step calculator. In the Import From Workspace dialog box, select . Addendo - If p : q = x : y, then the value of the ratio is p + q : x + y Subtrahendo - If p : q = x : y, then value of the ratio is p - q : x - y Dividendo - If p : q = x : y, then p - q : q = x - y : y Any three quantities are said to be in continued proportion if the ratio between the first and the second is equal to the ratio between the second and the third. For multiplication, use the * Solve for an unknown value with this fractions calculator. In case of any queries, you can reach back to us in the comments section, and we will try to solve them. Measures of Central Tendency: Definition & Examples. There are many properties of proportion, but here are the first 3: 1) If two ratios are equal, this is called a proportion. Of particular . Enter P 1 = 0.7 and P 2 = 0.75. In the expression, $m$ equals $2$ and $n$ equals $5$, Simplify $\left(y^3\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. But what if these basic Kingdom Monera is one of the Five Kingdom Classification based on cell structure, mode of nutrition and body organisation. Using it creatively, you can figure out other properties. Learn the properties of proportions in this free math video tutorial by Mario's Math Tutoring.0:09 What is a Proportion0:14 How to Solve Proportions0:22 Prop. Then hit "Calculate" and the test statistic and p-Value will be calculated for you. Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. (a) m E = 90 ( E and A are corresponding angles of similar polygons, and corresponding angles of similar polygons are equal.) This formula can be used to find the percent of a given ratio and to find the missing value of a part of a whole. Your email address will not be published. If you have two unknown variables, the cross multiplication concept can be used to check the proportion between two unknown variables. From the above example, we can say that product of extreme terms \( = 40 \times 350 = 14000\) and product of mean terms \( = 70 \times 200 = 14000\), Therefore, a product of extreme terms \(=\) product of mean terms. Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). In the above example, we have four values(10010)\Big(\dfrac{100}{10}\Big)(10100)and366=X10\dfrac{36}{6} = \dfrac{X}{10}636=10X Extremes are the values that form a downward slope (36 and 10 in this case). Please use consistent units for any input. Using the 68 95 99 Rule to Calculate Other Percentages. Solution: Let the fourth proportional be x. We observe \(2,\,4,\,16\) and \(64\) are in proportion because \(2:4 = 16:64.\). Algebraic expressions Calculator. The only exception is that division is not supported; Previous Properties of Proportions Next Similar Triangles Q.1: Are 36,49,6,7 in proportion?Ans: We have the product of extreme terms \( = 36 \times 7 = 252\)Product of means \( = 49 \times 6 = 294\)Therefore, the product of extreme terms \( \ne \) product of mean termsHence, \(36,49,6,7\) are not in proportion. In biology, flowering plants are known by the name angiosperms. At this rate, how many rotten mangoes will I have if l buy 100 mangoes?Ans: Suppose I have \(x\) rotten mangoes if I buy \(100\) mangoes. Your email address will not be published. \(a\) is called the first term or antecedent. . Invertendo If \(a : b = c : d\), then \(b : a = d : c\) Statology Study is the ultimate online statistics study guide that helps you study and practice all of the core concepts taught in any elementary statistics course and makes your life so much easier as a student. The Five Kingdom Classification system is a way of grouping living organisms. Your Mobile number and Email id will not be published. The procedure to use the proportion calculator is as follows: Step 1: Enter the ratios in the respective input field, Step 2: Now click the button Solve to get the result, Step 3: Finally, the true or false for the given proportion will be displayed in the output field. Required fields are marked *. In the expression, $m$ equals $3$ and $n$ equals $3$, Simplify $\left(y^4\right)^3$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. The proportion c,dc,dc,d and e,fe,fe,f would appear in the following way if the ratio layout is used. By specifying two numbers (A and B in the first fraction area) from the four numbers of the proportion (decimals are allowed) it will display the complete and true ratio by filling in the right values for the rest of two numbers (C and D); In case you input three numbers out of the four of the proportion (A, B AND either C or D) (decimals are allowed) it will display the ratio meaning that is returns the value for the number missing (C or D by case); Whenever you input all the components of the proportion it checks if the proportion is true or false. Proportion signifies the equal relationship between two or more ratios. Alternendo Property : If a/b = c/d, then a/c = b/d. Cross multiplying works because youre just multiplying both sides of the equation by 1. The easiest natural logarithms to calculate are: ln 1 = 0 since e = 1, and. In the expression a/b = c/d, a and b are in the same proportion as c and d. A proportion is typically set up to solve a word problem in which one of its four quantities is unknown. All rights reserved, Properties of Proportion: Types, Differences, Examples, All About Properties of Proportion: Types, Differences, Examples, JEE Advanced Previous Year Question Papers, SSC CGL Tier-I Previous Year Question Papers, SSC GD Constable Previous Year Question Papers, ESIC Stenographer Previous Year Question Papers, RRB NTPC CBT 2 Previous Year Question Papers, UP Police Constable Previous Year Question Papers, SSC CGL Tier 2 Previous Year Question Papers, CISF Head Constable Previous Year Question Papers, UGC NET Paper 1 Previous Year Question Papers, RRB NTPC CBT 1 Previous Year Question Papers, Rajasthan Police Constable Previous Year Question Papers, Rajasthan Patwari Previous Year Question Papers, SBI Apprentice Previous Year Question Papers, RBI Assistant Previous Year Question Papers, CTET Paper 1 Previous Year Question Papers, COMEDK UGET Previous Year Question Papers, MPTET Middle School Previous Year Question Papers, MPTET Primary School Previous Year Question Papers, BCA ENTRANCE Previous Year Question Papers, The numbers \(a,\,b,\,c\) and \(d\) are proportional if the ratio of the first two quantities is equal to the ratio of the last two quantities, i.e., \(a:b::c:d\) and is read as \(a\) is to \(b\) is as \(c\) is to \(d.\) The symbol \(::\) stands for is as.
, Each quantity in a proportion is called its term, or it is proportional. 2D shape calculators 3D shape calculators Prime numbers Number . 1. Some useful properties of ratio and proportion are invertendo property, alternendo property, componendo Property, dividendo property, convertendo property, componendo-dividendo property, addendo property and equivalent ratio property. When you have two ratios with values expected to be equal, certain steps of simplification are performed. Q.2: What are the types of proportion?Ans: There are two basic types of proportion, namely1. To solve fractions for unknown x using this proportion solver, follow the below steps: After pressing the button, you will get the value of unknown x and a step-by-step solution by cross multiplication and proportion method. In the expression, $m$ equals $4$ and $n$ equals $2$, Simplify $\left(\left(y^2\right)^4\right)^2$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. 1. The ratio formula for two numbers \(a\) and \(b\) is given by \(a:b\) or \(\mathbf{\frac{a}{b}}\). For instance, if the speed of a car is increased, it covers more distanceduring afixed amountof your time. If four numbers \(a,\,b,\,c,\,d\) are in proportion, we write \(a:b::c:d,\) which is read as \(a\) is to \(b\) as \(c\) is to \(d.\) Here, \(a\) is the first term, \(b\) is the second term, \(c\) is the third term, and \(d\) is the fourth term of the proportion. Step 4: Click on the "Reset" button to clear the fields and enter new values. If a sample of iron has a mass of 23.4 grams and a volume of 3.00 cm 3, the density of iron can be calculated as: d = m a s s v o l u m e d = 23.4 g 3.00 c m 3 = 7.80 g / c m 3 In this calculation, our two experimental numbers are 23.4 and 3.00. The reciprocal property of proportions. The first and fourth terms (a and d) are the "extremes." The second and third (b and c) are the . Similarly, four quantities in continued proportion will have the ratio between the first and second equal to the ratio between the third and fourth. We know how to calculate the surface area of the items in our surroundings. The output indicates that a total of 450 . Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Mean, Median & Mode Scientific . y which we can also express that as c / x = y / 1 and again solve for c. If y = 2 for x = 10, then we have c / 10 = 2 / 1 hence c = 20. The * is also optional when multiplying parentheses, example: (x + 1)(x 1). Thus, the continued proportion for the given ratios can be written in the form of \(ca:bc:bd\). { "@context": "https://schema.org", "@type": "FAQPage", "mainEntity": [{ "@type": "Question", "name": "What Is A Proportion? The ratio of a a to b b can also be expressed as a:b a: b or \dfrac {a} {b} ba. The power of a product is equal to the product of it's factors raised to the same power, Simplify $\left(x^2\right)^5$ using the power of a power property: $\left(a^m\right)^n=a^{m\cdot n}$. Q.5: For every 12 mangoes that I buy, 3 turn out to be rotten. 2 * 2 = 1 * 4 4 = 4
, For every proportion, the product of the extremes is always equal to the product of the means, i.e., \(p:q::r:s\) if and only if\(ps = qr.\)
, From the terms of a given proportion, we can make three more proportions. In our daily lives, we come across various cones of different shapes and sizes for which we can calculate surface area. We willstudythe properties of proportion calculator or how to calculate proportion. For example, consider two ratios to be a:b and c:d. In order to find the continued proportion for the two given ratio terms, we will convert their means to a single term/number. The test statistic is calculated as: z = (p-p 0) / (p0(1-p0)/n) where: p = observed sample proportion p 0 = hypothesized population proportion n = sample size Derivative calculator Integral calculator Definite integrator Limit calculator Series calculator Equation solver Expression simplifier Factoring calculator Expression calculator Inverse function Taylor series Matrix calculator Matrix arithmetic Graphing calculator. Step 1: Go to Cuemath's online proportions calculator. Hence, the following statement would be constructed after equating them. Alternendo If \(a : b = c : d\), then \(a : c = b: d\) Based on the type of relationship two or more quantities share, the proportion can be classified into different types. Polygon Calculator. Consider that the value of X needs to be determined in the equation given below. The Proportion Calculator is used to solve proportion problems and find the missing value in a proportion (Step by Step). A = 28, B = 34 and D =15 then C= 12.3529411765. Cross Product Property : The product of the extremes equals the product of the means. If both the numbers a and b are multiplied or divided by the same number in the ratio \(a:b\), then the resulting ratio remains the same as the original ratio. For example {eq}\frac {5} {10} {/eq} is proportional to {eq}\frac {1} {2} {/eq} and {eq}\frac {25} {50}. Draw a graph through the points to ascertain whether x and y values are in proportional relationship. Suppose the value of 'x' is unknown. if you enter only A and B in order to determine the C and D figures, it multiplies both A and B by 2 in order to return true ratio values for C and D. if you complete the A, B and C to find the D value, it solves the expression in which D = C * (B / A). $\frac{\left(\left(3x y^2\right)^4\left(2x^3 y^4\right)^3\right)^2}{\left(4x^2 y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(\left(3xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(\left(xy^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(2x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{4^5\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{\left(3^4\right)^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{81^2\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(2^3\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\left(x^4\right)^2\left(\left(y^2\right)^4\right)^28^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{6561\cdot 64\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024\left(x^2\right)^5\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}\left(y^3\right)^5}$, $\frac{419904\left(x^4\right)^2\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}\left(\left(y^2\right)^4\right)^2\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}\left(y^2\right)^{4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(\left(x^3\right)^3\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}\left(y^4\right)^3\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{2\cdot 5}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{3\cdot 5}}$, $\frac{419904x^{4\cdot 2}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{2\cdot 4\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{8\cdot 2}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{3\cdot 3}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{9}y^{4\cdot 3}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{16}\left(x^{9}y^{12}\right)^2}{1024x^{10}y^{15}}$, $\frac{419904x^{8}y^{\left(16-15\right)}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904x^{8}y^{1}\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904x^{8}y\left(x^{9}y^{12}\right)^2}{1024x^{10}}$, $\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{\left(10-8\right)}}$, $\frac{419904y\left(x^{9}y^{12}\right)^2}{1024x^{2}}$, $\frac{419904y\left(x^{9}\right)^2\left(y^{12}\right)^2}{1024x^{2}}$, $\frac{419904yx^{9\cdot 2}\left(y^{12}\right)^2}{1024x^{2}}$, $\frac{419904yx^{9\cdot 2}y^{12\cdot 2}}{1024x^{2}}$, $\frac{419904yx^{18}y^{12\cdot 2}}{1024x^{2}}$, $\frac{419904y^{\left(24+1\right)}x^{18}}{1024x^{2}}$, $\frac{419904y^{25}x^{\left(18-2\right)}}{1024}$, $\frac{\sqrt{2x^{12} y^{21} z^8}}{40\sqrt{xy\cdot z}}$, $\left(x\left(x^{2\left(x\left(x^2\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}}\right)^{\frac{1}{3}}\right)^{\frac{1}{3}}$, $\left(7x^{\frac{2}{3}}\left(x y^{121\left(-1\right)}\right)^{\frac{1}{2}}\right)^4$, $\left(1\left(81\right)\left(-1\right)\right)^{\frac{1}{4}}$, $\frac{\left(x^{\frac{1}{5}} y^{\frac{3}{2}}\right)^{10}}{\left(y^{\left(-1\right)\cdot\frac{2}{5}} x^{\frac{2}{3}}\right)^5}$, $\frac{\left(4x^{121\left(-1\right)} y^4 z^8\right)^3}{\left(9x y^3 z^5\right)^4}$, $\frac{\left(-5x^3 y^2\right)^3\left(x y^5\right)^2}{\left(-5x^{-1}\cdot y\right)^{-1}}$. 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