What is ((x^8y^{-4})/(16y^{4/3)})^{-1/4} ?

The solution to ((x^8y^{-4})/(16y^{4/3)})^{-1/4} is (2y^{4/3})/(x^2)

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simplify ((x^8y^{-4})/(16y^{4/3)})^{-1/4}

simplify

(\frac{x ^{8} y ^{- 4}}{16 y ^{\frac{4}{3}}})^{- \frac{1}{4}}

\frac{2 y ^{\frac{4}{3}}}{x ^{2}}

Solution steps

(\frac{x ^{8} y ^{- 4}}{16 y ^{\frac{4}{3}}})^{- \frac{1}{4}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

(\frac{x ^{8} y ^{- 4}}{16 y ^{\frac{4}{3}}})^{- \frac{1}{4}} = \frac{1}{( \frac{x ^{8} y ^{- 4}}{16 y ^{\frac{4}{3}}} ) ^{\frac{1}{4}}}

= \frac{1}{( \frac{x ^{8} y ^{- 4}}{16 y ^{\frac{4}{3}}} ) ^{\frac{1}{4}}}

Simplify

(\frac{x ^{8} y ^{- 4}}{16 y ^{\frac{4}{3}}})^{\frac{1}{4}} : \frac{x ^{2}}{2 y ^{\frac{4}{3}}}

= \frac{1}{\frac{x ^{2}}{2 y ^{\frac{4}{3}}}}

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

= \frac{2 y ^{\frac{4}{3}}}{x ^{2}}

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What is ((x^8y^{-4})/(16y^{4/3)})^{-1/4} ?
The solution to ((x^8y^{-4})/(16y^{4/3)})^{-1/4} is (2y^{4/3})/(x^2)