Intermediate Algebra (12th Edition)

$-\frac{5}{y}$
The quotient rule for radicals tells us that $\sqrt[n] \frac{a}{b}=\frac{\sqrt[n] a}{\sqrt[n] b}$ (if $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $n$ is a natural number). That is, the nth root of a quotient is the quotient of the nth roots. Therefore, $-\sqrt[4] \frac{625}{y^{4}}=-\frac{\sqrt[4] 625}{\sqrt[4] y^{4}}=-\frac{5}{y}$. $\sqrt[4] 625=5$, because $5^{4}=625$ $\sqrt[4] y^{4}=y$, because $(y)^{4}=y^{4}$