What is \sqrt[6]{(2u^{-3}v^4)^6} ?

The solution to \sqrt[6]{(2u^{-3}v^4)^6} is (2v^4)/(u^3)

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simplify \sqrt[6]{(2u^{-3}v^4)^6}

simplify

\frac{2 v ^{4}}{u ^{3}}

Solution steps

Apply radical rule:

assuming

a \geq 0

= 2 u^{- 3} v^{4}

Apply exponent rule:

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

u^{- 3} = \frac{1}{u ^{3}}

= 2 \cdot \frac{1}{u ^{3}} v^{4}

Apply the fraction rule:

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

= \frac{2 \cdot 1 \cdot v ^{4}}{u ^{3}}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{2 v ^{4}}{u ^{3}}

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What is \sqrt[6]{(2u^{-3}v^4)^6} ?
The solution to \sqrt[6]{(2u^{-3}v^4)^6} is (2v^4)/(u^3)