What is [[(2/3)^2]^3]^{-4} ?

The solution to [[(2/3)^2]^3]^{-4} is (3^{24})/(16777216)

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simplify [[(2/3)^2]^3]^{-4}

simplify

[(\frac{2}{3})^{2}]^{3}^{- 4}

\frac{3 ^{24}}{16777216}

Decimal Notation

16834.11219 \dots

Solution steps

[(\frac{2}{3})^{2}]^{3}^{- 4}

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

= [(\frac{2}{3})^{6}]^{- 4}

Apply exponent rule:

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

= \frac{1}{( ( \frac{2}{3} ) ^{6} ) ^{4}}

((\frac{2}{3})^{6})^{4} : (\frac{2}{3})^{24}

= \frac{1}{( \frac{2}{3} ) ^{24}}

Apply exponent rule:

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

(\frac{2}{3})^{24} = \frac{2 ^{24}}{3 ^{24}}

= \frac{1}{\frac{2 ^{24}}{3 ^{24}}}

Apply the fraction rule:

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

= \frac{3 ^{24}}{2 ^{24}}

2^{24} = 16777216

= \frac{3 ^{24}}{16777216}

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What is [[(2/3)^2]^3]^{-4} ?
The solution to [[(2/3)^2]^3]^{-4} is (3^{24})/(16777216)