Answer
$\color{blue}{81}$
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:
$27^{4/3} = \left(27^{1/3}\right)^4$
Use rule (2) above to obtain:
$=(\sqrt[3]{27})^4$
With $27=3^3$, the expression above is equivalent to:
$=(\sqrt[3]{3^3})^4$
Use rule (3) above to obtain"
$=(3)^4
\\=\color{blue}{81}$
