## anonymous 4 years ago I need to simplify this problem with radicals.

1. anonymous

$6x^6/\sqrt[3]{9^4}$

2. precal

$6x^6/\sqrt[3]{9*9*9*9}$ $6x^6/9\sqrt[3]{9}$ $2x^6/3\sqrt[3]{9}$

3. anonymous

My professor had gave me an answer of $2x^4\sqrt[3]{3^2}$. I am trying to understand how he came to this conclusion if you can explain it for me.

4. precal

are you sure it is division?

5. precal

$\sqrt[3]{9}$ is the same as $\sqrt[3]{3^2}$

6. anonymous

Yup, it is as I have given it to you.

7. precal

Are you sure you copied it correctly? You would be surprised how common that occurs.

8. anonymous

Bah, you're right. $6x^6/\sqrt[3]{9x^4}$ I had missed a variable.

9. anonymous

Sorry about that, he is one of the teachers that writes out his homework on a sheet a paper and makes copies of it.

10. precal

ok let me do it again

11. precal

$6x^6/\left( \sqrt[3]{9x^4}\right)$ $6x^6/\left( \sqrt[3]{9x*x*x*x}\right)$ $6x^6/\left( x\sqrt[3]{9x}\right)$ $6x^5/\left( \sqrt[3]{9x}\right)$

12. precal

Are you sure you wrote it correctly? We are using laws of exponents. The rules are pretty clear.