What is ((25x^4)/4)^{-1/2} ?

The solution to ((25x^4)/4)^{-1/2} is 2/(5x^2)

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simplify ((25x^4)/4)^{-1/2}

simplify

(\frac{25 x ^{4}}{4})^{- \frac{1}{2}}

\frac{2}{5 x ^{2}}

Solution steps

(\frac{25 x ^{4}}{4})^{- \frac{1}{2}}

Apply exponent rule:

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

(\frac{25 x ^{4}}{4})^{- \frac{1}{2}} = \frac{1}{( \frac{25 x ^{4}}{4} ) ^{\frac{1}{2}}}

= \frac{1}{( \frac{25 x ^{4}}{4} ) ^{\frac{1}{2}}}

Simplify

(\frac{25 x ^{4}}{4})^{\frac{1}{2}} : \frac{5 x ^{2}}{2}

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

Apply the fraction rule:

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

= \frac{2}{5 x ^{2}}

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