What is ((((2^3)/(5^3))^{-3})^2)^{-1/9} ?

The solution to ((((2^3)/(5^3))^{-3})^2)^{-1/9} is 4/25

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simplify ((((2^3)/(5^3))^{-3})^2)^{-1/9}

simplify

((\frac{2 ^{3}}{5 ^{3}})^{- 3})^{2}^{- \frac{1}{9}}

\frac{4}{25}

Decimal Notation

0.16

Solution steps

((\frac{2 ^{3}}{5 ^{3}})^{- 3})^{2}^{- \frac{1}{9}}

((\frac{2 ^{3}}{5 ^{3}})^{- 3})^{2} : (\frac{2 ^{3}}{5 ^{3}})^{- 6}

= ((\frac{2 ^{3}}{5 ^{3}})^{- 6})^{- \frac{1}{9}}

Apply exponent rule:

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

= \frac{1}{( ( \frac{2 ^{3}}{5 ^{3}} ) ^{- 6} ) ^{\frac{1}{9}}}

((\frac{2 ^{3}}{5 ^{3}})^{- 6})^{\frac{1}{9}} : (\frac{2 ^{3}}{5 ^{3}})^{- \frac{2}{3}}

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

Apply exponent rule:

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

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

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

Apply exponent rule:

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

(\frac{2 ^{3}}{5 ^{3}})^{\frac{2}{3}} = \frac{( 2 ^{3} ) ^{\frac{2}{3}}}{( 5 ^{3} ) ^{\frac{2}{3}}}

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

(5^{3})^{\frac{2}{3}} : 5^{2}

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

(2^{3})^{\frac{2}{3}} : 2^{2}

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

Apply the fraction rule:

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

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

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

Apply the fraction rule:

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

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

2^{2} = 4

= \frac{4}{5 ^{2}}

5^{2} = 25

= \frac{4}{25}

(2 x^{2} + 2 x + 2) \cdot (2 x^{2} + 2 x + 2)

\frac{x ^{2} + y ^{2}}{x ^{2} + y ^{2} + z ^{2}}

\frac{3}{2 3} \cdot \frac{3}{3}

e^{- (\frac{x}{2})^{2}}

What is ((((2^3)/(5^3))^{-3})^2)^{-1/9} ?
The solution to ((((2^3)/(5^3))^{-3})^2)^{-1/9} is 4/25