What is ((x^3y^{-2})/(xy))^{-1/5} ?

The solution to ((x^3y^{-2})/(xy))^{-1/5} is ((y^3)/(x^2))^{1/5}

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simplify ((x^3y^{-2})/(xy))^{-1/5}

simplify

(\frac{x ^{3} y ^{- 2}}{x y})^{- \frac{1}{5}}

(\frac{y ^{3}}{x ^{2}})^{\frac{1}{5}}

Solution steps

(\frac{x ^{3} y ^{- 2}}{x y})^{- \frac{1}{5}}

Apply exponent rule:

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

(\frac{x ^{3} y ^{- 2}}{x y})^{- \frac{1}{5}} = \frac{1}{( \frac{x ^{3} y ^{- 2}}{x y} ) ^{\frac{1}{5}}}

= \frac{1}{( \frac{x ^{3} y ^{- 2}}{x y} ) ^{\frac{1}{5}}}

Simplify

(\frac{x ^{3} y ^{- 2}}{x y})^{\frac{1}{5}} : (\frac{x ^{2}}{y ^{3}})^{\frac{1}{5}}

= \frac{1}{( \frac{x ^{2}}{y ^{3}} ) ^{\frac{1}{5}}}

(\frac{x ^{2}}{y ^{3}})^{\frac{1}{5}} = \frac{x ^{\frac{2}{5}}}{y ^{\frac{3}{5}}}

= \frac{1}{\frac{x ^{\frac{2}{5}}}{y ^{\frac{3}{5}}}}

Apply the fraction rule:

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

= \frac{y ^{\frac{3}{5}}}{x ^{\frac{2}{5}}}

Combine same powers :

\frac{x ^{\frac{a}{m}}}{y ^{\frac{b}{m}}} = (\frac{x ^{a}}{y ^{b}})^{\frac{1}{m}}

= (\frac{y ^{3}}{x ^{2}})^{\frac{1}{5}}

y^{2} - 3 y - 9 = 0

3 z + 1 = 2 z

- \frac{1}{5} - 1

\frac{x}{5} + \frac{x}{3} + 7 = 15

3 \cdot 1063

What is ((x^3y^{-2})/(xy))^{-1/5} ?
The solution to ((x^3y^{-2})/(xy))^{-1/5} is ((y^3)/(x^2))^{1/5}