Question

How do you simplify 5/3rd root of 26^2?

Answer 1

`root(5/3)(26^2) = (26^2)^(3/5) = 26^(6/5)`

Explanation:

The `n`th root of a number `a` is `a^(1/n)`

So the `5/3`rd root of a number `a` is `a^(3/5)`

In addtion, if `a > 0` and `b, c != 0`, then `(a^b)^c = a^(bc)`

So:

`root(5/3)(26^2) = (26^2)^(3/5) = 26^(2*3/5) = 26^(6/5)`

This cannot be simplified further since `26` has no fifth power factors.