Question

PLEASE HELP!!!

How is $\sqrt[7]{x^5} *\sqrt[7]{x^5}$ equal too $x\sqrt[7]{x^3}$ ? Please write the steps and properties of how you obtain $x\sqrt[7]{x^3}$ as a result of the equation.

Answer 1

First combine the roots:

$\sqrt[7]{x^5}\cdot\sqrt[7]{x^5}=\sqrt[7]{x^5\cdot x^5}=\sqrt[7]{x^{10}}$

Now use the fact that $\sqrt[n]{x^n}=x$ (for odd $n$):

$\sqrt[7]{x^{10}}=\sqrt[7]{x^7\cdot x^3}=\sqrt[7]{x^7}\cdot\sqrt[7]{x^3}=x\sqrt[7]{x^3}$