Given x > 0 and y > 0, select the expression that is equivalent to root(4)(256x^(16)y^(12)) 64x^((1)/(4))y^((1)/(3)) 64x^(4)y^(3) 4x^(4)y^(3) 4x^((1)/(4))y^((1)/(3))

Identify Given Expression: Identify the given expression and the operation to be performed. We need to find the fourth root of 256x^(16)y^(12).Simplify Constant: Simplify the constant within the fourth root. The fourth root of 256 is 4, because 4^4 = 256.Simplify Variable x: Simplify the variable x with the exponent under the fourth root. The fourth root of x^(16) is x^(16/4), which simplifies to x^4.Simplify Variable y: Simplify the variable y with the exponent under the fourth root. The fourth root of y^(12) is y^(12/4), which simplifies to y^3.Combine Simplified Parts: Combine the simplified parts of the expression. The equivalent expression is 4x^4y^3.

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Q. Given

x>0

and

y>0

, select the expression that is equivalent to

\newline

\sqrt[4]{256 x^{16} y^{12}}

\newline

64 x^{\frac{1}{4}} y^{\frac{1}{3}}

\newline

64 x^{4} y^{3}

\newline

4 x^{4} y^{3}

\newline

4 x^{\frac{1}{4}} y^{\frac{1}{3}}

Identify Given Expression: Identify the given expression and the operation to be performed. $\newline$ We need to find the fourth root of $256x^{16}y^{12}$ .
Simplify Constant: Simplify the constant within the fourth root. The fourth root of $256$ is $4$ , because $4^4 = 256$ .
Simplify Variable $x$ : Simplify the variable $x$ with the exponent under the fourth root. The fourth root of $x^{16}$ is $x^{\frac{16}{4}}$ , which simplifies to $x^4$ .
Simplify Variable $y$ : Simplify the variable $y$ with the exponent under the fourth root. The fourth root of $y^{12}$ is $y^{\frac{12}{4}}$ , which simplifies to $y^3$ .
Combine Simplified Parts: Combine the simplified parts of the expression. $\newline$ The equivalent expression is $4x^4y^3$ .