Answer
$\color{blue}{-27}$
Work Step by Step
RECALL:
(1) $a^{m/n} = \left(^{1/n}\right)^m$
(2) $a^{1/n} = \sqrt[n]{a}$
(3) For positive real numbers $a$, $\sqrt[n]{a^n}=a$
Use rule (1) above to obtain:
$-81^{3/4} = -\left(81^{1/4}\right)^3$
Use rule (2) above to obtain:
$=-(\sqrt[4]{81})^3$
With $81=3^4$, the expression above is equivalent to:
$=-(\sqrt[4]{3^4})^3$
Use rule (3) above to obtain"
$=-(3)^3
\\=\color{blue}{-27}$
