Answer
$(-64)^{1/4}$ is not a real number
Work Step by Step
RECALL:
(1) $a^{1/4} = \sqrt[4]{a}$
(2) $\sqrt[4]{16} = 2$ since $2^4=16$
(3) For any real number $a$, $a^4 \ge 0$.
Use rule (1) above to obtain:
$(-64)^{1/4} = \sqrt[4]{-64}$
Note that there is no real number that when raised to the 4th power will give $-64$ since when a real number is raised to the 4th power, the result is always non-negative.
Thus,
$(-64)^{1/4}$ is not a real number
