Answer
$\dfrac{1}{8}$
Work Step by Step
RECALL:
(i) $a^{-\frac{m}{n}}=\dfrac{1}{a^{\frac{m}{n}}}$
(ii) $a^{\frac{m}{n}}=\sqrt[n]{a^m}$
Use the rules above to obtain:
$=\dfrac{1}{16^{\frac{3}{4}}}
\\=\dfrac{1}{\sqrt[4]{16^3}}
\\=\dfrac{1}{\sqrt[4]{(2^4)^3}}
\\=\dfrac{1}{\sqrt[4]{2^{12}}}
\\=\dfrac{1}{\sqrt[4]{(2^{3})^4}}
\\=\dfrac{1}{2^3}
\\=\dfrac{1}{8}$
