Rewrite the following expressions without using radicals or negative exponents. Simplify when possible. root(5)(x^20y^-4)

Emily-Jane Bray 2021-01-17 Answered

Rewrite the following expressions without using radicals or negative exponents. Simplify when possible.

\sqrt[5]{x^{20} y^{- 4}}

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dessinemoie

Answered 2021-01-18 Author has 90 answers

The given radical can be rewritten as,

\sqrt[5]{x^{20} y^{- 4}} = {(x^{20} y^{- 4})}^{\frac{1}{5}} ⟨ . \sqrt[n]{a} = {(a)}^{\frac{1}{n}}

The radical can be further simplified as,

\sqrt[5]{x^{20} y^{- 4}} = {(x^{20} y^{- 4})}^{\frac{1}{5}} = {(x^{20})}^{\frac{1}{5}} \cdot {(y^{- 4})}^{\frac{1}{5}} = x^{4} y^{- \frac{4}{5}} = {(x y^{- \frac{1}{5}})}^{4}

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