Q:

# What are exponents with fractions?

A:

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.

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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.

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