Given x > 0 and y > 0, select the expression that is equivalent to sqrt(64x^(8)y^(5)) 32x^(4)y^((5)/(2)) 32x^((1)/(4))y^((2)/(5)) 8x^((1)/(4))y^((2)/(5)) 8x^(4)y^((5)/(2))

Identify expression: Identify the expression to simplify. We need to simplify the square root of the expression 64x^(8)y^(5).Simplify 64: Simplify the square root of 64. The square root of 64 is 8 because 8 * 8 = 64.Simplify x^(8): Simplify the square root of x^(8). The square root of x^(8) is x^(4) because (x^(4))^2 = x^(8).Simplify y^(5): Simplify the square root of y^(5). The square root of y^(5) is y^((5/2)) because (y^((5/2)))^2 = y^(5).Combine results: Combine the simplified parts. Combine the results from steps 2, 3, and 4 to get the simplified expression: 8x^(4)y^((5/2)).

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Q. Given

x>0

and

y>0

, select the expression that is equivalent to

\newline

\sqrt{64 x^{8} y^{5}}

\newline

32 x^{4} y^{\frac{5}{2}}

\newline

32 x^{\frac{1}{4}} y^{\frac{2}{5}}

\newline

8 x^{\frac{1}{4}} \boldsymbol{y}^{\frac{2}{5}}

\newline

8 x^{4} y^{\frac{5}{2}}

Identify expression: Identify the expression to simplify. $\newline$ We need to simplify the square root of the expression $64x^{8}y^{5}$ .
Simplify $64$ : Simplify the square root of $64$ . The square root of $64$ is $8$ because $8 \times 8 = 64$ .
Simplify $x^{8}$ : Simplify the square root of $x^{8}$ . $\newline$ The square root of $x^{8}$ is $x^{4}$ because $(x^{4})^2 = x^{8}$ .
Simplify $y^{5}$ : Simplify the square root of $y^{5}$ . The square root of $y^{5}$ is $y^{\left(\frac{5}{2}\right)}$ because $\left(y^{\left(\frac{5}{2}\right)}\right)^2 = y^{5}$ .
Combine results: Combine the simplified parts. $\newline$ Combine the results from steps $2$ , $3$ , and $4$ to get the simplified expression: $8x^{4}y^{(5/2)}$ .