What is [[(2/3)^2]^3]^{-1} ?

The solution to [[(2/3)^2]^3]^{-1} is 729/64

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simplify [[(2/3)^2]^3]^{-1}

simplify

[(\frac{2}{3})^{2}]^{3}^{- 1}

\frac{729}{64}

Decimal Notation

11.390625

Solution steps

[(\frac{2}{3})^{2}]^{3}^{- 1}

[(\frac{2}{3})^{2}]^{3} : (\frac{2}{3})^{6}

= [(\frac{2}{3})^{6}]^{- 1}

Apply exponent rule:

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

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

Apply exponent rule:

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

(\frac{2}{3})^{6} = \frac{2 ^{6}}{3 ^{6}}

= \frac{1}{\frac{2 ^{6}}{3 ^{6}}}

Apply the fraction rule:

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

= \frac{3 ^{6}}{2 ^{6}}

3^{6} = 729

= \frac{729}{2 ^{6}}

2^{6} = 64

= \frac{729}{64}

4712.38898 \cdot 1 0^{- 9}

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