Answer
$\dfrac{1}{243}$
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:
$=\dfrac{1}{81^{\frac{5}{4}}}
\\=\dfrac{1}{\sqrt[4]{81^5}}
\\=\dfrac{1}{\sqrt[4]{(3^4)^5}}
\\=\dfrac{1}{\sqrt[4]{3^{20}}}
\\=\dfrac{1}{\sqrt[4]{(3^{5})^4}}
\\=\dfrac{1}{3^5}
\\=\dfrac{1}{243}$
