Answer
$2x^3\sqrt{10x}$
Work Step by Step
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $
\dfrac{\sqrt{400x^{10}}}{\sqrt{10x^3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{400x^{10}}{10x^3}}
\\\\=
\sqrt{\dfrac{40x^7\cdot\cancel{10x^3}}{\cancel{10x^3}}}
\\\\=
\sqrt{40x^7}
\\\\=
\sqrt{4x^6\cdot10x}
\\\\=
\sqrt{(2x^3)^2\cdot10x}
\\\\=
2x^3\sqrt{10x}
.\end{array}
Note that variables are assumed to have positive real numbers.
