Question

The expression \sqrt[5]{v^{25}}

Answer 1

Does it ask to simplify the expression?

Answer 2

yes i need to simplify the expression

Answer 3

\[
v^{25} = (v^5)^5
\]

Answer 4

\[
v^{25} =v^{5\times 5} = (v^5)^5
\]So:\[
\sqrt[5]{v^{25}} = \sqrt[5]{(v^5)^5} = v^5
\]

Answer 5

In general: \[
\sqrt[a]{v^b} = v^{b/a}
\]Which in this case where \(a=5\) and \(b=25\): \[
\sqrt[5]{v^{25}} = v^{25/5} = v^5
\]

Answer 6

thanx