Assuming that $x, y, z$ are positive real numbers, simplify each of the following:$(\sqrt{x^{-3}})^{5}$
Given:
$(\sqrt{x^{-3}})^{5}$
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,
$(\sqrt{x^{-3}})^{5}=(x^{\frac{-3}{2}})^5$
$=(x)^{\frac{-3}{2}\times5}$
$=(x)^{\frac{-15}{2}}$
$=\frac{1}{(x)^{\frac{15}{2}}}$
Hence, $(\sqrt{x^{-3}})^{5}=\frac{1}{(x)^{\frac{15}{2}}}$.
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