Question

How do you simplify `(6^(2/3)*4^(2/3))/3^(2/3)`?

Answer 1

`4`

Explanation:

In this case all the indices are the same, although the bases are different.

You can combine all the factors into a single base:

`(6^color(red)(2/3)xx 4^color(red)(2/3))/3^color(red)(2/3) " "=" " ((6xx4)/3)^color(red)(2/3)`

`= 8^color(red)(2/3)`

`= (root(3)(8))^2`

`=2^2 = 4`