You said you were having issues with the math language. You've been shown what is equivalent to what, but not an explanation of which is called by which name (the language.)
ax is where x is the exponent
So 23 has an exponent of 3.
A fractional exponent is the same thing, except the x is going to be a fraction like:
Which is 2 to the 1/3rd. The (1/3) is the exponent and it's a fraction; hence, fractional exponent.
A radical is with the √ sign. So square root, cubed root, etc are radicals. Like:
x√a means the x root of a.
2√16 means the square root of 16 (which is 4). (Usually just written as √16 with the 2 being understood. That only works when it's just a 2.)
A fractional exponent can be written as a radical. As already shown:
x√(ay ) means x root of (ay)
2(1/3) (fractional exponent) can be written as 3√2 (radical)
4(2/3) (fractional exponent) can be written as 3√(42) (radical)
Note where the numerator and denominator of the fraction in the exponent are when you do it as a radical. (numerator inside and denominator outside) When the numerator is 1, you don't write it. In my example 2(1/3) =
3√2 note I never put the 1 exponent on the radical. 21 = 2 so the 1 is not needed and we leave it off.
You have to decide which is easier to solve. :-) If you're doing it manually, you just about have to turn it into a radical. (2 multiplied times itself 1/3 times? Sounds a little weird, huh?) If you're using a calculator either can be just as easy depending
on the calculator. But I suspect since you're just learning these, you're doing them manually.
That's probably a lot very quickly, but once you're getting into radicals, they "assume" you already know how to do the exponents.