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}

(\frac{11}{12})^{2}

x^{2} + 10 x = 6

(x) (x + 1) = 2970

0 = - 16 t^{2} + 16 t + 32

[\frac{( x + 3 )}{( x + 8 )}] \geq 6

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