Question

How do you rewrite with fractional exponents for `(root(3)(2))(root(3)(ab))`?

Answer 1

`(root(3)(2))(root(3)(ab)) = (2^(1/3))((ab)^(1/3))" or " (2ab)^(1/3)`

Explanation:

SInce `b^m*b*n*b*p = b^(m+n+p)`
then `b^(1/3) * b^(1/3) * b^(1/3) = b^1`

also `root(3)(b) * root(3)(b) * root(3)(b) = b^1`

So `root(3)(b)` is the same as `b^(1/3)`

Replacing `b` with `2` and then with `ab` lets us derive the given solution.