## Algebra: A Combined Approach (4th Edition)

$\frac{1}{y^{30}}$
We know that $a^{−n}=\frac{1}{a^{n}}$ and $\frac{1}{a^{-n}}=a^{n}$ (as long as a is a nonzero real number and n is an integer). Therefore, $\frac{y^{-10}}{(y^{5})^{4}}=\frac{y^{-10}}{y^{5\times4}}=\frac{y^{-10}}{y^{20}}=\frac{1}{y^{10}}\times \frac{1}{y^{20}}=\frac{1}{y^{10+20}}=\frac{1}{y^{30}}$.