## Introductory Algebra for College Students (7th Edition)

$4x^4\sqrt{5x}$
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.