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

The solution to (x^{-2}-y^{-1})^{-3} is (x^6y^3)/((y-x^2)^3)

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

simplify

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

\frac{x ^{6} y ^{3}}{( y - x ^{2} ) ^{3}}

Solution steps

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

Apply exponent rule:

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

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

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

Simplify

(x^{- 2} - y^{- 1})^{3} : \frac{( y - x ^{2} ) ^{3}}{x ^{6} y ^{3}}

= \frac{1}{\frac{( y - x ^{2} ) ^{3}}{x ^{6} y ^{3}}}

Apply the fraction rule:

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

= \frac{x ^{6} y ^{3}}{( y - x ^{2} ) ^{3}}

3 \frac{1}{2} \div \frac{1}{2}

2^{99} + 2^{99}

- (- 2) + 1

\frac{1}{2 π \cdot 100 \cdot 1 0 ^{- 9} \cdot 51000}

\frac{x ^{2} - 3 x}{8 x}

What is (x^{-2}-y^{-1})^{-3} ?
The solution to (x^{-2}-y^{-1})^{-3} is (x^6y^3)/((y-x^2)^3)