Answer
$2x^2\sqrt{5}$
Work Step by Step
RECALL:
(1) The quotient rule:
$\dfrac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\dfrac{a}{b}}$
where
$\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers and $b\ne0$
(2) $\dfrac{a^m}{a^n} = a^{m-n}, a \ne =0$
Use the quotient rule above to obtain:
$\require{cancel}=\sqrt{\dfrac{200x^3}{10x^{-1}}}
\\=\sqrt{\dfrac{20\cancel{200}x^3}{\cancel{10}x^{-1}}}
\\=\sqrt{\dfrac{20x^3}{x^{-1}}}$
Use rule (2) above to obtain:
$=\sqrt{20x^{3-(-1)}}
\\=\sqrt{20x^{3+1}}
\\=\sqrt{20x^4}$
Factor the radicand so that at least one factor is a perfect square to obtain:
$=\sqrt{4x^4(5)}
\\=\sqrt{(2x^2)^2(5)}$
Simplify to obtain:
$=2x^2\sqrt{5}$
