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Popular >

simplify ((5^{-2})/(5^{-1)})^{-4}

Solution

simplify

(\frac{5 ^{- 2}}{5 ^{- 1}})^{- 4}

Solution

625

Solution steps

(\frac{5 ^{- 2}}{5 ^{- 1}})^{- 4}

Apply exponent rule:

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

(\frac{5 ^{- 2}}{5 ^{- 1}})^{- 4} = \frac{1}{( \frac{5 ^{- 2}}{5 ^{- 1}} ) ^{4}}

= \frac{1}{( \frac{5 ^{- 2}}{5 ^{- 1}} ) ^{4}}

(\frac{5 ^{- 2}}{5 ^{- 1}})^{4} = \frac{1}{625}

= \frac{1}{\frac{1}{625}}

\frac{1}{\frac{1}{625}} = 625

= 625

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Frequently Asked Questions (FAQ)

What is ((5^{-2})/(5^{-1)})^{-4} ?
The solution to ((5^{-2})/(5^{-1)})^{-4} is 625