# Thread: Powers inside roots? [surds]

1. ## Powers inside roots? [surds]

Hello, how do I simplify powers that are inside roots? Example: say x is a positive number (I don't know how to write the math on a PC sorry)

sq< 9x^8
[Square root of nine and x to the power of 8]

To simplify, I can square root 9 to get 3, and take that to the outside of the root.

3 sq< x^8

But what about the x to the power of 8? I have no idea

2. Originally Posted by RAz
Hello, how do I simplify powers that are inside roots? Example: say x is a positive number (I don't know how to write the math on a PC sorry)

sq< 9x^8
[Square root of nine and x to the power of 8]

To simplify, I can square root 9 to get 3, and take that to the outside of the root.

3 sq< x^8

But what about the x to the power of 8? I have no idea

$\displaystyle \sqrt{9x^8}$

it's like this $\displaystyle (\sqrt{3x^4})^2$ then cancel exponent $\displaystyle ^2$ with the root

then it's like this $\displaystyle =3x^4$

after 3 then divide 8 by 2 that's what

remember
in roots you will divide $\displaystyle \sqrt{2^6}= 2^{\frac{6}{2}}$

in division you will subtract $\displaystyle \frac{x^4}{x^2}= x^{4-2}$

3. Thanks!

4. you're very welcome!