Answer
$\color{blue}{512}$
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:
$64^{3/2} = \left(64^{1/2}\right)^3$
Use rule (2) above to obtain:
$=(\sqrt[2]{64})^3$
With $64=8^2$, the expression above is equivalent to:
$=(\sqrt[2]{8^2})^3$
Use rule (3) above to obtain"
$=(8)^3
\\=\color{blue}{512}$
