Answer
$=\sqrt[6] { a^{ 5}b^{4} } $.
Work Step by Step
The given expression is
$\sqrt[6] {ab^2} \cdot \sqrt[3] {a^2b}$
Use $\sqrt[n] x=x^{\frac{1}{n}}$.
$=\left ( ab^2 \right )^{\frac{1}{6}} \cdot \left ( a^2b \right )^{\frac{1}{3}}$
Use $(ab)^m=a^mb^m$.
$= a^{\frac{1}{6} }b^{2\cdot \frac{1}{6}} \cdot a^{2\cdot \frac{1}{3}}b ^{\frac{1}{3}}$
$= a^{ \frac{1}{6} }b^{\frac{1}{3}} \cdot a^{\frac{2}{3}}b ^{\frac{1}{3}}$
Use $a^m\cdot a^n=a^{m+n}$
$= a^{ \frac{1}{6}+\frac{2}{3} }b^{\frac{1}{3}+\frac{1}{3}} $
$= a^{ \frac{1+4}{6}}b^{\frac{1+1}{3}} $
$= a^{ \frac{5}{6}}b^{\frac{2}{3}} $.
$= a^{ \frac{5}{6}}b^{\frac{4}{6}} $.
$= \left ( a^{ 5}b^{4} \right )^{\frac{1}{6}} $.
Use $x^{\frac{1}{n}}=\sqrt[n] x$.
$=\sqrt[6] { a^{ 5}b^{4} } $.
