# Rewrite the following expressions without using radicals or negative exponents.

Rewrite the following expressions without using radicals or negative exponents. Simplify when possible. $\sqrt[5]{{x}^{20}{y}^{-4}}$
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The given radical can be rewritten as,
$\sqrt[5]{{x}^{20}{y}^{-4}}={\left({x}^{20}{y}^{-4}\right)}^{\frac{1}{5}}\left(\because \sqrt[n]{a}={\left(a\right)}^{\frac{1}{n}}\right)$
The radical can be further simplified as,
$\sqrt[5]{{x}^{20}{y}^{-4}}={\left({x}^{20}\right)}^{\frac{1}{5}}{\left({y}^{-4}\right)}^{\frac{1}{5}}\left(\because {\left(ab\right)}^{n}={a}^{n}\cdot {b}^{n}\right)$
=${x}^{4}{y}^{-\frac{4}{5}}\left({\left({a}^{n}\right)}^{b}={a}^{nb}\right)$
=${\left(x{y}^{-\frac{1}{5}}\right)}^{4}$