What is \sqrt[6]{a^2b}^4sqrt(ab) ?

The solution to \sqrt[6]{a^2b}^4sqrt(ab) is a^{11/6}b^{2/3}sqrt(b)

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simplify \sqrt[6]{a^2b}^4sqrt(ab)

simplify

a^{\frac{11}{6}} b^{\frac{2}{3}} b

Solution steps

= (a^{2} b)^{\frac{2}{3}} ab

(a^{2} b)^{\frac{2}{3}} : a^{\frac{4}{3}} b^{\frac{2}{3}}

= a^{\frac{4}{3}} b^{\frac{2}{3}} ab

Apply radical rule:

ab = a b

= a^{\frac{4}{3}} b^{\frac{2}{3}} a b

Apply exponent rule:

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

a^{\frac{4}{3}} a = a^{\frac{4}{3}} a^{\frac{1}{2}} = a^{\frac{4}{3} + \frac{1}{2}}

= b^{\frac{2}{3}} a^{\frac{4}{3} + \frac{1}{2}} b

a^{\frac{4}{3} + \frac{1}{2}} = a^{\frac{11}{6}}

= a^{\frac{11}{6}} b^{\frac{2}{3}} b

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What is \sqrt[6]{a^2b}^4sqrt(ab) ?
The solution to \sqrt[6]{a^2b}^4sqrt(ab) is a^{11/6}b^{2/3}sqrt(b)