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(1)/((root(5)(-32))^(-3))

$\frac{1}{(\sqrt[5]{-32})^{-3}}$

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Evaluate rational exponents

Full solution

Q.

\frac{1}{(\sqrt[5]{-32})^{-3}}

Identify Base and Exponent: Identify the base and the exponent in the expression $(\sqrt[5]{-32})^{-3}$ . $\newline$ Base: $-32$ $\newline$ Exponent: $-3$
Express $-32$ as Term: Express $-32$ as a term raised to the power of $5$ . $-32 = -(2 \times 2 \times 2 \times 2 \times 2) = -(2^5)$
Rewrite Using Fifth Root: Rewrite the expression using the fifth root and the negative exponent. $\newline$ $(1)/((\sqrt[5]{-32})^{(-3)})$ $\newline$ = $(1)/((-(2^5))^{(1/5)})^{(-3)}$ $\newline$ = $(1)/((-2)^{(-3)})$
Simplify Negative Exponent: Simplify the negative exponent by taking the reciprocal. $\newline$ $(1)/((-2)^{-3})$ $\newline$ = $(-2)^3$
Calculate Value: Calculate the value of $(-2)^3$ . $\newline$ $(-2)^3 = -2 \times -2 \times -2$ $\newline$ $= -8$

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