Question

simplified form of fifth root of x times the fifth root of x times the fifth root of x times the fifth root of x?

Answer 1

\[\large \sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}~~?\]
Remember, \(\large \sqrt[n]{x}=x^{1/n}\), and \(\large \left(x^n\right)^m=x^{mn}\), so
\[\large \sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}\cdot\sqrt[5]{x}=\left(x^{1/5}\right)^4=x^{4/5}=\sqrt[5]{x^4}\]