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

$\dfrac{10\sqrt{3}}{y^{15}}$
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $\sqrt{\dfrac{300}{y^{30}}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt{300}}{\sqrt{y^{30}}} \\\\= \dfrac{\sqrt{100\cdot3}}{\sqrt{y^{30}}} \\\\= \dfrac{\sqrt{(10)^2\cdot3}}{\sqrt{(y^{15})^2}} \\\\= \dfrac{10\sqrt{3}}{y^{15}} .\end{array} Note that variables are assumed to have positive real numbers.