Our aim here is to recognize and factor out terms which are 5th powers, so that they can be simplified using the 5th-root.

`root(5)(8a^3b^4) root(5)(8a^2b^3)`

We first multiply out the expressions under the 5th roots.

` = root(5)((8a^3b^4)(8a^2b^3))`

`= root(5)(64a^5b^7)`

Then we look for numbers or algebraic terms for which we can find the 5th root.

`=root(5)(32a^5b^5) root(5)(2b^2)`

Then we find those fifth roots, and leave the `2b^2` under the 5th root sign because we cannot do any more with it.

`=2ab root(5)(2b^2) `