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Popular >

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

Solution

simplify

Solution

8

Solution steps

Apply radical rule:

= (3 2^{\frac{1}{- 5}})^{- 3}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= 3 2^{\frac{1}{- 5} (- 3)}

\frac{1}{- 5} (- 3) = \frac{3}{5}

= 3 2^{\frac{3}{5}}

Factor the number:

32 = 2^{5}

= (2^{5})^{\frac{3}{5}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

(2^{5})^{\frac{3}{5}} = 2^{5 \cdot \frac{3}{5}} = 2^{3}

= 2^{3}

Refine

= 8

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Frequently Asked Questions (FAQ)

What is (\sqrt[-5]{32})^{-3} ?
The solution to (\sqrt[-5]{32})^{-3} is 8