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}

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}

36 - 4 x^{2}

\frac{- 1}{3}

x^{2} = - 18 x

- 12 x^{2} = 34 x - 28

200 = \frac{1}{2} (3) x^{2}

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