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