Answer
$a-a^{2}$
Work Step by Step
Using the laws of exponents, the given expression, $
a^{-1/4}\left( a^{5/4}-a^{9/4} \right)
,$ simplifies to
\begin{array}{l}\require{cancel}
a^{\frac{-1}{4}+\frac{5}{4}}-a^{\frac{-1}{4}+\frac{9}{4}}
\\\\=
a^{\frac{4}{4}}-a^{\frac{8}{4}}
\\\\=
a^{1}-a^{2}
\\\\=
a-a^{2}
.\end{array}
