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Simplify:$ \left(16^{-1 / 5}\right)^{5 / 2} $
Given:
\( \left(16^{-1 / 5}\right)^{5 / 2} \)
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,
$(16^{-1 / 5})^{5 / 2}=[[2^{4}]^{\frac{-1}{5}}]^{\frac{5}{2}}$
$=2^{4 \times \frac{-1}{5} \times \frac{5}{2}}$
$=2^{-2}$
$=\frac{1}{2^{2}}$
$=\frac{1}{4}$
Hence, $(16^{-1 / 5})^{5 / 2}=\frac{1}{4}$.
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