What is ((3/5)^4*(3/5)^{-3}+1)^{-1/3} ?

The solution to ((3/5)^4*(3/5)^{-3}+1)^{-1/3} is (5^{1/3})/2

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simplify ((3/5)^4*(3/5)^{-3}+1)^{-1/3}

simplify

((\frac{3}{5})^{4} \cdot (\frac{3}{5})^{- 3} + 1)^{- \frac{1}{3}}

\frac{5 ^{\frac{1}{3}}}{2}

Decimal Notation

0.85498 \dots

Solution steps

((\frac{3}{5})^{4} (\frac{3}{5})^{- 3} + 1)^{- \frac{1}{3}}

Apply exponent rule:

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

((\frac{3}{5})^{4} (\frac{3}{5})^{- 3} + 1)^{- \frac{1}{3}} = \frac{1}{( ( \frac{3}{5} ) ^{4} ( \frac{3}{5} ) ^{- 3} + 1 ) ^{\frac{1}{3}}}

= \frac{1}{( ( \frac{3}{5} ) ^{4} ( \frac{3}{5} ) ^{- 3} + 1 ) ^{\frac{1}{3}}}

((\frac{3}{5})^{4} (\frac{3}{5})^{- 3} + 1)^{\frac{1}{3}} = \frac{2}{5 ^{\frac{1}{3}}}

= \frac{1}{\frac{2}{5 ^{\frac{1}{3}}}}

Apply the fraction rule:

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

= \frac{5 ^{\frac{1}{3}}}{2}

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What is ((3/5)^4*(3/5)^{-3}+1)^{-1/3} ?
The solution to ((3/5)^4*(3/5)^{-3}+1)^{-1/3} is (5^{1/3})/2