rewrite using radical notation?

Question

(2ab)4/5

Answer 1

There are two ways to write this. Unfortunately, they can't be fully illustrated using ASCII characters.

One way is this:

4√(2ab)^5.

The 4 denotes an index (4th root extraction) of the final expression under the radical. The 4 would actually be placed over the hook and just to the left of the radical symbol. The power of 5 would be applied to the expression under the radical symbol. In this example, the expression is raised to the 5th power first, and then its 4th root is extracted.

Another way is this:

[4√(2ab)]^5.

The 4 is used as an index like before to extract the 4th root, but that is done first. Then the 4th root is raised to the 5th power.

Answer 2

5th root of (2^4a^4b^4) = 5th root of (16a^4b^4)

The denominator is always the root. I remember that the roots are at the bottom of the tree; the roots are at the bottom of the exponent :-)