What is ((2^{-4})/(2^{-2)})^{-1} ?

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

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simplify ((2^{-4})/(2^{-2)})^{-1}

simplify

(\frac{2 ^{- 4}}{2 ^{- 2}})^{- 1}

4

Solution steps

(\frac{2 ^{- 4}}{2 ^{- 2}})^{- 1}

Apply exponent rule:

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

(\frac{2 ^{- 4}}{2 ^{- 2}})^{- 1} = \frac{1}{\frac{2 ^{- 4}}{2 ^{- 2}}}

= \frac{1}{\frac{2 ^{- 4}}{2 ^{- 2}}}

Apply the fraction rule:

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

= \frac{2 ^{- 2}}{2 ^{- 4}}

Apply exponent rule:

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

\frac{2 ^{- 2}}{2 ^{- 4}} = 2^{- 2 - (- 4)}

= 2^{- 2 - (- 4)}

Subtract the numbers:

- 2 - (- 4) = 2

= 2^{2}

2^{2} = 4

= 4

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What is ((2^{-4})/(2^{-2)})^{-1} ?
The solution to ((2^{-4})/(2^{-2)})^{-1} is 4