Answer
$4x^4\sqrt{5x}$
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{800x^{12}}}{\sqrt{10x^3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{800x^{12}}{10x^3}}
\\\\=
\sqrt{\dfrac{80x^9\cdot\cancel{10x^3}}{\cancel{10x^3}}}
\\\\=
\sqrt{80x^9}
\\\\=
\sqrt{16x^8\cdot5x}
\\\\=
\sqrt{(4x^4)^2\cdot5x}
\\\\=
4x^4\sqrt{5x}
.\end{array}
Note that variables are assumed to have positive real numbers.
