Answer
$-\frac{5a\sqrt { 6ab}}{b^3}$.
Work Step by Step
The given expression is
$=-\sqrt {\frac{150a^3}{b^5}}$
Use the quotient rule and rewrite as the quotient of radicals.
$=-\frac{\sqrt {150a^3}}{\sqrt {b^5}}$
Factor each term as a perfect square.
$=-\frac{\sqrt {5^2\cdot 6a^2a}}{\sqrt {b^4b}}$
Simplify.
$=-\frac{5a\sqrt { 6a}}{b^2\sqrt {b}}$
Multiply the numerator and denominator by $\sqrt b$ to remove the radical in the denominator.
$=-\frac{5a\sqrt { 6a}}{b^2\sqrt {b}}\cdot \frac{\sqrt b}{\sqrt b}$
Multiply.
$=-\frac{5a\sqrt { 6ab}}{b^2\sqrt {b^2}}$
Simplify.
$=-\frac{5a\sqrt { 6ab}}{b^3}$.
