Answer
J. Not a real number
Work Step by Step
As shown on page 445, we know that $a^{\frac{m}{n}}=\sqrt[n] a^{m}=(\sqrt[n] a)^{m}$.
Therefore, $(-25)^{\frac{1}{2}}=\sqrt[2] (-25)^{1}=\sqrt -25=$ not a real number.
We know this because there is no number $a$, such that $a^{2}=-25$.
