Answer
$\sqrt[12] { a^{ 10}b^{7} } $.
Work Step by Step
The given expression is
$\sqrt[4] {a^2b} \cdot \sqrt[3] {ab}$
Use $\sqrt[n] x=x^{\frac{1}{n}}$.
$=\left ( a^2b \right )^{\frac{1}{4}} \cdot \left ( ab \right )^{\frac{1}{3}}$
Use $(ab)^m=a^mb^m$.
$= a^{2\cdot \frac{1}{4} }b^{\frac{1}{4}} \cdot a^{\frac{1}{3}}b ^{\frac{1}{3}}$
$= a^{ \frac{1}{2} }b^{\frac{1}{4}} \cdot a^{\frac{1}{3}}b ^{\frac{1}{3}}$
Use $a^m\cdot a^n=a^{m+n}$
$= a^{ \frac{1}{2}+\frac{1}{3} }b^{\frac{1}{4}+\frac{1}{3}} $
$= a^{ \frac{3+2}{6}}b^{\frac{3+4}{12}} $
$= a^{ \frac{5}{6}}b^{\frac{7}{12}} $.
$= a^{ \frac{10}{12}}b^{\frac{7}{12}} $.
$= \left ( a^{ 10}b^{7} \right )^{\frac{1}{12}} $.
Use $x^{\frac{1}{n}}=\sqrt[n] x$.
$=\sqrt[12] { a^{ 10}b^{7} } $.
