Answer
$\frac{a\sqrt{a}}{7}$.
Work Step by Step
The given expression is
$=\sqrt{\frac{a^3}{49}}$
Use quotient property of square roots.
$=\frac{\sqrt{a^3}}{\sqrt{49}}$
Use $49=7^2$ and $a^3=a^2\cdot a$.
$=\frac{\sqrt{a^2\cdot a}}{\sqrt{7^2}}$
Use product property of square roots.
$=\frac{\sqrt{a^2}\cdot \sqrt{a}}{\sqrt{7^2}}$
Simplify.
$=\frac{a\sqrt{a}}{7}$.
