What are exponents with fractions?

If an exponent is a fraction, such as y^1/n, the correct operation is to take the nth root of the base number y. For example, 27^1/3 is the same thing as taking the cube root of 27, so the answer is 3.

When like numbers with exponents are multiplied, the product is found by adding the exponents together. For example, 3^2 x 3^3 = 3^5. It follows that 9^1/2 x 9^1/2 = 9^(1/2 + 1/2) or 9^1 = 9. This means (9^1/2)2 = 9, which is equivalent to saying that squaring the square root of a number yields the original number. Therefore, 9^1/2 is equivalent to taking the square root of 9.