Review the first two lines of Marco's work for solving an equation.

Line 1: LaTeX: \sqrt[5]{x+7}=3
√
[
5
]
x
+
7
=
3
[
5
]
x
+
7
=
3

Line 2: LaTeX: \left(x+7\right)^{^{\frac{1}{5}}}=3

What did Marco do in line 2? Why was he allowed to make this change to the radical expression? Be sure to support your answer with mathematical reasoning.