Answer
$\dfrac{1}{1024}$
Work Step by Step
RECALL:
(i) $a^{\frac{m}{n}}=(\sqrt[n]{a})^m.$
(ii) $a^{-m} = \dfrac{1}{a^m}, a\ne0.$
Use rule (ii) above to obtain
$\dfrac{1}{16^{\frac{5}{2}}}.$
Use rule (i) with m=5 and n=2 to obtain
$\dfrac{1}{(\sqrt{16})^5}
\\=\dfrac{1}{(\sqrt{4^2})^5}
\\=\dfrac{1}{(4)^5}
\\=\dfrac{1}{1024}.$
