Given x 0 and y 0, select the expression that is equivalent to root(4)(81x^(18)y^(8)) 9x^((2)/(9))y^((1)/(2)) 9x^((9)/(2))y^(2) 3x^((2)/(9))y^((1)/(2)) 3x^((9)/(2))y^(2)

Question

Given  x > 0 and  y > 0, select the expression that is equivalent to  root(4)(81x^(18)y^(8))  9x^((2)/(9))y^((1)/(2))  9x^((9)/(2))y^(2)  3x^((2)/(9))y^((1)/(2))  3x^((9)/(2))y^(2)

Bytelearn · Accepted Answer

Identify Given Expression: Identify the given expression and the operation to be performed. The given expression is the fourth root of 81x^(18)y^(8), which can be written as (81x^(18)y^(8))^(1/4).Rewrite as Product of Powers: Rewrite the expression inside the root as a product of powers. 81 is a perfect square and can be written as 3^4. Also, x^(18) and y^(8) can be written as (x^(18/4)) and (y^(8/4)) respectively. (81x^(18)y^(8))^(1/4) = (3^4 * x^(18) * y^(8))^(1/4)Apply Exponent Property: Apply the property of exponents which states that (a^m)^n = a^(m*n) to simplify the expression. (3^4 * x^(18) * y^(8))^(1/4) = 3^(4*(1/4)) * x^(18*(1/4)) * y^(8*(1/4))Simplify Exponents: Simplify the exponents by multiplying them. 3^(4*(1/4)) = 3^1 = 3 x^(18*(1/4)) = x^(18/4) = x^(4.5) = x^(9/2) y^(8*(1/4)) = y^(8/4) = y^2Combine Simplified Terms: Combine the simplified terms to get the final expression. The equivalent expression is 3 * x^(9/2) * y^2.Check Answer Choices: Check the answer choices to see which one matches the simplified expression. The correct answer choice is 3x^((9)/(2))y^(2).

Given x>0 and y>0 , select the expression that is equivalent to $\newline$ $\sqrt[4]{81 x^{18} y^{8}}$ $\newline$ $9 x^{\frac{2}{9}} y^{\frac{1}{2}}$ $\newline$ $9 x^{\frac{9}{2}} y^{2}$ $\newline$ $3 x^{\frac{2}{9}} y^{\frac{1}{2}}$ $\newline$ $3 x^{\frac{9}{2}} y^{2}$

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