What is (2u^2v^3)^3(3u^{-3}v)^2 ?

The solution to (2u^2v^3)^3(3u^{-3}v)^2 is 72v^{11}

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simplify (2u^2v^3)^3(3u^{-3}v)^2

simplify

(2 u^{2} v^{3})^{3} (3 u^{- 3} v)^{2}

72 v^{11}

Solution steps

(2 u^{2} v^{3})^{3} (3 u^{- 3} v)^{2}

Simplify

(2 u^{2} v^{3})^{3} : 8 u^{6} v^{9}

= 8 u^{6} v^{9} (3 u^{- 3} v)^{2}

Simplify

(3 u^{- 3} v)^{2} : \frac{9 v ^{2}}{u ^{6}}

= 8 u^{6} v^{9} \frac{9 v ^{2}}{u ^{6}}

Cross-cancel common factor:

u^{6}

= 8 v^{9} \cdot 9 v^{2}

Multiply the numbers:

8 \cdot 9 = 72

= 72 v^{9} v^{2}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

v^{9} v^{2} = v^{9 + 2}

= 72 v^{9 + 2}

Add the numbers:

9 + 2 = 11

= 72 v^{11}

\frac{2}{2} + \frac{1 - 2}{- 1}

- 25 a^{2} + 185 a - 70

\frac{1}{4} x - \frac{1}{5} x + \frac{1}{20} x = 4

4 - c = 5

\frac{3}{4} = \frac{x}{20}

What is (2u^2v^3)^3(3u^{-3}v)^2 ?
The solution to (2u^2v^3)^3(3u^{-3}v)^2 is 72v^{11}