Have you ever seen rational exponents? Rational exponents are designed to fit within the properties of exponents. That is, (31/2)2 is equal to 31, or 3. What operation does the power 1/2 represent? Can you think of operations that other fractional powers represent, such as 1/3, 1/4 and 2/3?

Rational exponents are quite simple really.  For instance, 2 to the power of 1/2 is the square root of two.  You take the numerator of the fraction and use that as the exponent and take the denominator and use it to root the number.  I know that sounds confusing, so I'll give a bunch of examples

2 to the power of 1/3

is the cube root of 2

2 to the power of 2/3

is the cube root of 2 to the power of 2, or the cube root of 4

2 to the power of 3/4

Is the 4th root of 2 to the power of 3, or the fourth root of 8

Hope it helps <3, if you have any questions just comment.

Step-by-step explanation:

(31/2)2 is equal to 31, or 3, BUT there is no rational exponent here.  

The power 1/2, as in x^(1/2), is equivalent to the square root of the base.

For example, 9^(1/2) = sqrt(9) = ±3.  

9^(1/3) is the CUBE root of 9, which (using a calculator) is approximately

2.08.

9^(1/5) represents the 5th root of 9, which is approximately 1.55.

And so on.