Answer
$\dfrac{1}{10\sqrt{10}}$
Work Step by Step
RECALL:
(i) $a^{\frac{m}{n}} =\sqrt[n]{a^m}$
(i) $a^{-m} = \dfrac{1}{a^m}, a\ne0$
Use rule (ii) above to obtain:
$=\dfrac{1}{a^{\frac{3}{2}}}$
Use rule (i) above, where m=3 and n=2, to obtain:
$=\dfrac{1}{\sqrt{10^3}}$
Factor the radicand so that one factor is a square, then simplify to obtain:
$=\dfrac{1}{\sqrt{10^2 \cdot 10}}
\\=\dfrac{1}{10\sqrt{10}}$
