What is ((625/256)^-)^{3/4} ?

The solution to ((625/256)^-)^{3/4} is 64/125

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simplify ((625/256)^-)^{3/4}

simplify

((\frac{625}{256})^{-})^{\frac{3}{4}}

\frac{64}{125}

Decimal Notation

0.512

Solution steps

((\frac{625}{256})^{-})^{\frac{3}{4}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}

= (\frac{625}{256})^{- \frac{3}{4}}

Apply exponent rule:

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

= \frac{1}{( \frac{625}{256} ) ^{\frac{3}{4}}}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{625}{256})^{\frac{3}{4}} = \frac{62 5 ^{\frac{3}{4}}}{25 6 ^{\frac{3}{4}}}

= \frac{1}{\frac{62 5 ^{\frac{3}{4}}}{25 6 ^{\frac{3}{4}}}}

25 6^{\frac{3}{4}} = 64

= \frac{1}{\frac{62 5 ^{\frac{3}{4}}}{64}}

62 5^{\frac{3}{4}} = 125

= \frac{1}{\frac{125}{64}}

Apply the fraction rule:

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

= \frac{64}{125}

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