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}`