Answer
$\dfrac{(x-1)(x-7)}{x^{3/2}}$ or $\dfrac{(x-1)(x-7)}{\sqrt{x^{3}}}$ or $x^{-3/2}(x-1)(x-7)$
Work Step by Step
$7x^{-3/2}-8x^{-1/2}+x^{1/2}$
Take out common factor $x^{-3/2}$:
$7x^{-3/2}-8x^{-1/2}+x^{1/2}=x^{-3/2}(7-8x+x^{2})=...$
Rearrange:
$...=x^{-3/2}(x^{2}-8x+7)=...$
Factor the expression inside the parentheses:
$...=x^{-3/2}(x-1)(x-7)=...$
Rearrange again:
$...=\dfrac{(x-1)(x-7)}{x^{3/2}}$