From Förberedande kurs i matematik 1

The expression \displaystyle \sqrt{\text{7}^{\text{5}}\text{ }} can be written as \displaystyle (\text{7}^{\text{5}})^{\text{1}/\text{2}}\text{ } and then the power rules give that this is equal to

\displaystyle 7^{5\centerdot \frac{1}{2}}=7^{{5}/{2}\;}