Answer
$ \displaystyle \frac{1}{2p^{2}}$
Work Step by Step
$\displaystyle \frac{8p^{-3}(4p^{2})^{-2}}{p^{-5}} \qquad$ ....... use $(ab)^{m}=a^{m} b^{m}$
$=\displaystyle \frac{8p^{-3}\cdot 4^{-2}(p^{2})^{-2}}{p^{-5}}$
....... use $(a^{m})^{n}=a^{mn}$, group like terms
$=8\displaystyle \cdot 4^{-2}\cdot\frac{p^{-3}\cdot p^{-4}}{p^{-5}}$
....... use $a^{m}\cdot a^{n}=a^{m+n} ,\quad \displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
.......recognize: $8=2^{3},\quad 4=2^{2}$
$=(2^{3})(2^{2})^{-2}\cdot p^{-3-4-(-5)}\qquad$ ....... use $(a^{m})^{n}=a^{mn}$
$=(2^{3})(2^{-4})\cdot p^{-2}\qquad$ ....... use $a^{m}\cdot a^{n}=a^{m+n}$
$=2^{3-4}p^{-2}$
$=2^{-1}p^{-2}\qquad$ ....... use $a^{-n}=\displaystyle \frac{1}{a^{n}}=(\frac{1}{a})^{n}$
$= \displaystyle \frac{1}{2p^{2}}$
