Answer
$\dfrac{10\sqrt{3}}{y^{15}}$
Work Step by Step
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.
