Answer
$5x^2\sqrt{2}$
Work Step by Step
$\frac{\sqrt{500x^{3}}}{{\sqrt{10x^{-1}}}}$
By the quotient rule for square roots
$=\sqrt{\frac{500x^{3}}{10x^{-1}}}$
$=\sqrt{50x^{3-(-1)}}$
$=\sqrt{50x^{(3+1)}}$
$=\sqrt{50x^{4}}$
$=\sqrt{25\cdot 2 \cdot x^{4}}$
$=\sqrt{25} \cdot \sqrt{x^{4}} \cdot \sqrt{2}$
$=5x^{2}\sqrt{2}$
