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Simplify. $\newline$ $32^{(-1/5)}$

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Evaluate rational exponents

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Q. Simplify.

\newline

32^{(-1/5)}

Identify Base & Exponent: Identify the base and the exponent in $32^{(-1/5)}$ . $\newline$ Base: $32$ $\newline$ Exponent: $-1/5$
Rewrite as Power of $2$ : Rewrite $32$ as a power of $2$ because $32$ is $2$ raised to the $5$ th power. $\newline$ $32 = 2^5$
Apply Power Rule: Apply the power of a power rule: $(a^m)^n = a^{(m*n)}$ . $\newline$ So, $(2^5)^{-\frac{1}{5}}$ becomes $2^{(5*(-\frac{1}{5}))}$ .
Multiply Exponents: Multiply the exponents: $5*(-1/5)$ equals $-1$ . So, $2^{5*(-1/5)}$ simplifies to $2^{-1}$ .
Simplify to Reciprocal Form: Simplify $2^{-1}$ to its reciprocal form. $\newline$ $2^{-1}$ equals $\frac{1}{2}$ .

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