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

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

Question
Exponents and radicals
asked 2021-01-17
Rewrite the following expressions without using radicals or negative exponents. Simplify when possible. \(\displaystyle{\sqrt[{{5}}]{{{x}^{{20}}{y}^{{-{{4}}}}}}}\)

Answers (1)

2021-01-18
The given radical can be rewritten as,
\(\displaystyle{\sqrt[{{5}}]{{{x}^{{20}}{y}^{{-{{4}}}}}}}={\left({x}^{{20}}{y}^{{-{{4}}}}\right)}^{{\frac{{1}}{{5}}}}{\left\langle.{\sqrt[{{n}}]{{{a}}}}={\left({a}\right)}^{{\frac{{1}}{{n}}}}\right.}\)
The radical can be further simplified as,
\(\displaystyle{\sqrt[{{5}}]{{{x}^{{20}}{y}^{{-{{4}}}}}}}={\left({x}^{{20}}{y}^{{-{{4}}}}\right)}^{{\frac{{1}}{{5}}}}={\left({x}^{{20}}\right)}^{{\frac{{1}}{{5}}}}\cdot{\left({y}^{{-{{4}}}}\right)}^{{\frac{{1}}{{5}}}}={x}^{{4}}{y}^{{-\frac{{4}}{{5}}}}={\left({x}{y}^{{-\frac{{1}}{{5}}}}\right)}^{{4}}\)
image
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