What is (x^{-3}+y^{-2})^{-1} ?

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

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simplify (x^{-3}+y^{-2})^{-1}

simplify

(x^{- 3} + y^{- 2})^{- 1}

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

Solution steps

(x^{- 3} + y^{- 2})^{- 1}

Apply exponent rule:

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

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

= \frac{1}{x ^{- 3} + y ^{- 2}}

Simplify

x^{- 3} + y^{- 2} : \frac{1}{x ^{3}} + \frac{1}{y ^{2}}

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

Join

\frac{1}{x ^{3}} + \frac{1}{y ^{2}} : \frac{y ^{2} + x ^{3}}{x ^{3} y ^{2}}

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

Apply the fraction rule:

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

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

\frac{- 20}{- 5}

(2 x^{3} - 9)^{3}

- 2 - 21

\frac{( x + a ) ^{2} - x ^{2}}{a}

(5 w^{3} y - 7 w)^{2}

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