I had a question in my calculus book that was written a little strangely and I tried to rewrite it to be more simple but it did not work out. It made me realize something about powers and radicals though.
If I have $\sqrt{2^2}$ that is like $2^{2* \frac{1}{2}}$ if I am correct. I was thinking that I could cancel them out somehow but I doesn't really seem to be useful ever because they are reverse operations. For example if I have something more complex like
$2^{3*\frac{1}{5}}$ I can't really cancel anything out can I? Even though it is like I am multiplying $2*2*2$ and also diving by $2*2*2*2*2$ I can only make it a power of $\frac{3}{5}$ correct?
I guess what I am asking is that there is no simpler way to do work with this is there? If I have a power and a radical they aren't applied similar to $2^2 * 2^5$ where I just add the powers, I actually have to multiply powers because it is more like (for the power and radical example) $(2^2)^ \frac{1}{5}$ where I would then multiply out the powers.