What is (2^{-2}-5^{-1})^{-1} ?

The solution to (2^{-2}-5^{-1})^{-1} is 20

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simplify (2^{-2}-5^{-1})^{-1}

simplify

(2^{- 2} - 5^{- 1})^{- 1}

20

Solution steps

(2^{- 2} - 5^{- 1})^{- 1}

Apply exponent rule:

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

(2^{- 2} - 5^{- 1})^{- 1} = \frac{1}{2 ^{- 2} - 5 ^{- 1}}

= \frac{1}{2 ^{- 2} - 5 ^{- 1}}

Simplify

2^{- 2} - 5^{- 1} : \frac{1}{2 ^{2}} - \frac{1}{5}

= \frac{1}{\frac{1}{2 ^{2}} - \frac{1}{5}}

Join

\frac{1}{2 ^{2}} - \frac{1}{5} : \frac{1}{20}

= \frac{1}{\frac{1}{20}}

Apply the fraction rule:

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

= \frac{20}{1}

Apply rule

\frac{a}{1} = a

= 20

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