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

The solution to [(x^2y^{-2})^{-1}]^{-1} is (x^2)/(y^2)

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simplify [(x^2y^{-2})^{-1}]^{-1}

simplify

[(x^{2} y^{- 2})^{- 1}]^{- 1}

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

Solution steps

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

- 1 \cdot (- 1) = 1

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

Apply exponent rule:

a^{1} = a

= x^{2} y^{- 2}

Apply exponent rule:

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

y^{- 2} = \frac{1}{y ^{2}}

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{1 \cdot x ^{2}}{y ^{2}}

Multiply:

1 \cdot x^{2} = x^{2}

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

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