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

$\dfrac{\sqrt{13}}{x^3}$
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $\sqrt{\dfrac{13}{x^6}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt{13}}{\sqrt{x^6}} \\\\= \dfrac{\sqrt{13}}{\sqrt{(x^3)^2}} \\\\= \dfrac{\sqrt{13}}{x^3} .\end{array} Note that variables are assumed to have positive real numbers.