What is ((a^2)^{-1})^{-2} ?

The solution to ((a^2)^{-1})^{-2} is a^4

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simplify ((a^2)^{-1})^{-2}

simplify

((a^{2})^{- 1})^{- 2}

a^{4}

Solution steps

((a^{2})^{- 1})^{- 2}

(a^{2})^{- 1} : a^{- 2}

= (a^{- 2})^{- 2}

Apply exponent rule:

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

= \frac{1}{( a ^{- 2} ) ^{2}}

(a^{- 2})^{2} : a^{- 4}

= \frac{1}{a ^{- 4}}

Apply exponent rule:

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

a^{- 4} = \frac{1}{a ^{4}}

= \frac{1}{\frac{1}{a ^{4}}}

Apply the fraction rule:

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

= \frac{a ^{4}}{1}

Apply the fraction rule:

\frac{a}{1} = a

= a^{4}

\frac{x ^{2}}{( x - 1 ) ^{2}}

8 x y (x^{3} y)

\frac{60}{- 15}