I need to simplify this problem with radicals.

Question

anonymous · Answer

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

precal · Answer

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

anonymous · Answer

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.

precal · Answer

are you sure it is division?

precal · Answer

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

anonymous · Answer

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

precal · Answer

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

anonymous · Answer

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

anonymous · Answer

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

precal · Answer

ok
let me do it again

precal · Answer

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

precal · Answer

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