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Given
x > 0, the expression
root(8)(x^(32)) is equivalent to

x^(5)root(8)(x^(6))

x^(5)

x^(4)root(8)(x^(6))

x^(4)

Given x>0 , the expression $\sqrt[8]{x^{32}}$ is equivalent to $\newline$ $x^{5} \sqrt[8]{x^{6}}$ $\newline$ $x^{5}$ $\newline$ $x^{4} \sqrt[8]{x^{6}}$ $\newline$ $x^{4}$

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Multiplication with rational exponents

Full solution

Q. Given

x>0

, the expression

\sqrt[8]{x^{32}}

is equivalent to

\newline

x^{5} \sqrt[8]{x^{6}}

\newline

x^{5}

\newline

x^{4} \sqrt[8]{x^{6}}

\newline

x^{4}

Given Expression Simplification: We are given the expression $\sqrt[8]{x^{32}}$ and we need to simplify it. The $8$ th root of $x$ to the power of $32$ can be written as $x^{\frac{32}{8}}$ because in general, $\sqrt[n]{x^m} = x^{\frac{m}{n}}$ .
Exponent Simplification: Now we simplify the exponent by dividing $32$ by $8$ . This gives us $x^{(32/8)} = x^4$ .
Comparison for Equivalent Expression: We compare the simplified expression $x^4$ with the given options to find the equivalent expression. The correct equivalent expression is $x^4$ .

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