# How do you simplify (root5(47))^5?

Mar 23, 2018

47

#### Explanation:

Just how if you square a square root, you get the radicand, if you take the fifth root and raise it to the fifth power, you get the radicand, which is 47 in this case.

$\sqrt[5]{47} = {47}^{\frac{1}{5}}$

$\implies {\left({47}^{\frac{1}{5}}\right)}^{5}$

Applying, color(red)((a^m)^n= a^(mn)

$\implies {47}^{\frac{1}{5} \times 5} = 47$