What is {[(2/3)^3]^{-2}}^4*((12)/(2^5*3^9))^{-5} ?

The solution to {[(2/3)^3]^{-2}}^4*((12)/(2^5*3^9))^{-5} is (3^{64})/(512)

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simplify {[(2/3)^3]^{-2}}^4((12)/(2^53^9))^{-5}

simplify

⎩ ⎨ ⎧ [(\frac{2}{3})^{3}]^{- 2} ⎭ ⎬ ⎫^{4} \cdot (\frac{12}{2 ^{5} \cdot 3 ^{9}})^{- 5}

\frac{3 ^{64}}{512}

Decimal Notation

6.70641 E 27

Solution steps

⎩ ⎨ ⎧ [(\frac{2}{3})^{3}]^{- 2} ⎭ ⎬ ⎫^{4} (\frac{12}{2 ^{5} \cdot 3 ^{9}})^{- 5}

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

= {(\frac{2}{3})^{- 6}}^{4} (\frac{12}{2 ^{5} \cdot 3 ^{9}})^{- 5}

Apply exponent rule:

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

= \frac{1}{( \frac{12}{3 ^{9} \cdot 2 ^{5}} ) ^{5}} {(\frac{2}{3})^{- 6}}^{4}

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

= \frac{3 ^{24}}{2 ^{24}} \cdot \frac{1}{( \frac{12}{3 ^{9} \cdot 2 ^{5}} ) ^{5}}

\frac{1}{( \frac{12}{2 ^{5} \cdot 3 ^{9}} ) ^{5}} = 3^{40} \cdot 2^{15}

= 3^{40} \cdot 2^{15} \cdot \frac{3 ^{24}}{2 ^{24}}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 ^{24} \cdot 3 ^{40} \cdot 2 ^{15}}{2 ^{24}}

3^{24} \cdot 3^{40} \cdot 2^{15} = 3^{64} \cdot 2^{15}

= \frac{3 ^{64} \cdot 2 ^{15}}{2 ^{24}}

Apply exponent rule:

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

\frac{2 ^{15}}{2 ^{24}} = \frac{1}{2 ^{24 - 15}}

= \frac{3 ^{64}}{2 ^{24 - 15}}

Subtract the numbers:

24 - 15 = 9

= \frac{3 ^{64}}{2 ^{9}}

2^{9} = 512

= \frac{3 ^{64}}{512}

3.4 \cdot 1 0^{- 9}

(x y^{2}) (3 x^{2} y^{2}) (2 x)

e^{- t} sin (sin (3 t))

258.15 \cdot 1 0^{2} \cdot 10

What is {[(2/3)^3]^{-2}}^4*((12)/(2^5*3^9))^{-5} ?
The solution to {[(2/3)^3]^{-2}}^4*((12)/(2^5*3^9))^{-5} is (3^{64})/(512)