What is ((2/3)^6)^{-4} ?

The solution to ((2/3)^6)^{-4} is (3^{24})/(16777216)

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simplify ((2/3)^6)^{-4}

simplify

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

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

Decimal Notation

16834.11219 \dots

Solution steps

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

6 (- 4) = - 24

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

Apply exponent rule:

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

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

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

(\frac{2}{3})^{24} = \frac{16777216}{3 ^{24}}

= \frac{1}{\frac{16777216}{3 ^{24}}}

Apply the fraction rule:

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

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

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