Answer
$2x^{2}\sqrt{5}$
Work Step by Step
$\frac{\sqrt{200x^{3}}}{{\sqrt{10x^{-1}}}}$
By the quotient rule for square roots
$=\sqrt{\frac{200x^{3}}{10x^{-1}}}$
$=\sqrt{20x^{3-(-1)}}$
$=\sqrt{20x^{(3+1)}}$
$=\sqrt{20x^{4}}$
$=\sqrt{4 \cdot 5 \cdot x^{4}}$
$=\sqrt{4} \cdot \sqrt{x^{4}} \cdot \sqrt{5}$
$=2x^{2}\sqrt{5}$
