Rational exponents and Radicals
By Marc Bibian
Radicals to Rational exponents
Lets say we are trying to solve the problem on the right but you don't know how we got answer so first what you want to do is look at the root and you see the little 3 on the outside that means its a cubed root so now you want to see the variable or number inside the root and its x^2 so now you know everything that's going on in the problem. So now you can convert the radical to a rational exponent so the number on the outside that's right next to the root will always be the denominator in the exponent of the number or variable and the number inside or the square will always be the numerator. Finally you leave X alone and just get rid of the square root and convert to a rational exponent so you'll take the 3 and put it as the denominator and take the 2 as the numerator and you'll have the exponent fraction of 2/3 and add that to the X and you'll have X^2/3 so that's how we got our answer on the right.
Rational exponents to Radicals
This is basically the opposite of Radicals to Rational exponents so lets say we have 5^1/2 to get this to a radical just convert by putting your denominator which is 2 and putting it right outside the square root or just leave it as a normal square root. Next we'll put the 5 inside the square root with the exponent of 1 or just 5 because the numerator of the power will always be the square in the root. So we'll have the square root of 5 as our answer. That's how we convert rational exponents to radicals.
Converting radicals (roots) to fractional (rational) exponents
Ma10 4.4 (2) Fractional Exponents and Radicals