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Popular >

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

Solution

simplify

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

Solution

\frac{1}{100}

+1

Decimal Notation

0.01

Solution steps

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

(\frac{1}{2})^{4} = \frac{1}{16}

= \frac{1}{16} (\frac{5}{2})^{- 2}

Apply exponent rule:

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

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

= \frac{1}{16} \cdot \frac{1}{( \frac{5}{2} ) ^{2}}

(\frac{5}{2})^{2} = \frac{25}{4}

= \frac{1}{16} \cdot \frac{1}{\frac{25}{4}}

Apply the fraction rule:

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

= \frac{1}{16} \cdot \frac{4}{25}

\frac{1}{16} \cdot \frac{4}{25} = \frac{1}{100}

= \frac{1}{100}

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Frequently Asked Questions (FAQ)

What is (1/2)^4*(5/2)^{-2} ?
The solution to (1/2)^4*(5/2)^{-2} is 1/100