#### Answer

$(-4)^{1/2}$ is not a real number

#### Work Step by Step

RECALL:
(1) $a^{1/2} = \sqrt{a}$
(2) $\sqrt{9} = 3$ since $3^2=9$
(3) For any real number $a$, $a^2 \ge 0$.
Use rule (1) above to obtain:
$(-4)^{1/2} = \sqrt{-4}$
Note that there is no real number that when squared will give $-4$ since when a real number is squared, the result is always non-negative.
Thus,
$(-4)^{1/2}$ is not a real number