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

$5x^6\sqrt{3x}$
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $\sqrt{15x^4}\cdot\sqrt{5x^9} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{15x^4(5x^9)} \\\\= \sqrt{75x^{13}} \\\\= \sqrt{25x^{12}\cdot3x} \\\\= \sqrt{(5x^{6})^2\cdot3x} \\\\= 5x^6\sqrt{3x} .\end{array} Note that variables are assumed to have positive real numbers.