Answer
$\sqrt{p^{7}q^{3}}-\sqrt{p^{5}q^{9}}+\sqrt{p^{9}q}=p^{2}(pq-q^{4}+p^{2})\sqrt{pq}$
Work Step by Step
$\sqrt{p^{7}q^{3}}-\sqrt{p^{5}q^{9}}+\sqrt{p^{9}q}$
Evaluate each square root:
$\sqrt{p^{7}q^{3}}-\sqrt{p^{5}q^{9}}+\sqrt{p^{9}q}=...$
$...=p^{3}q\sqrt{pq}-p^{2}q^{4}\sqrt{pq}+p^{4}\sqrt{pq}=...$
The expressions inside square roots are all the same. Simplify by taking out common factor $\sqrt{pq}$:
$...=(p^{3}q-p^{2}q^{4}+p^{4})\sqrt{pq}$
Take out common factor $p^{2}$ from the expression inside parentheses:
$...=p^{2}(pq-q^{4}+p^{2})\sqrt{pq}$
