Simplify:$ \sqrt[5]{(32)^{-3}} $

Given:

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

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

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

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

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

$=(2)^{-3}$

$=\frac{1}{2^3}$

$=\frac{1}{8}$

Hence, $\sqrt[5]{(32)^{-3}}=\frac{1}{8}$. 

Tutorialspoint

Updated on: 10-Oct-2022

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