When working with equations, whenever you change something on one side of the equation, you must perform an equal operation on the other side of the equation. If your equation contains fractional, or rational, exponents, work step by step to simplify the equation on each side so that it no longer contains the exponents.
Use the Reciprocal
To get rid of the fractional exponent, first raise both sides of the equation to the reciprocal of the exponent, then simplify the equation and solve. For example, start with the equation x^(5/2) = 32. This means x to the power of 5/2 equals 32. The reciprocal of 5/2 is 2/5. Raising both sides, you have x^(5/2)^(2/5) = 32^(2/5).
Simplify the Left Side
When you raise one exponent by another, you multiply the exponents. To simplify the left side of the equation to its equivalent, multiply 5/2 by 2/5: x^(5/2)^(2/5) = x^(5/2 * 2/5) = x^1 = x.
Simplify the Right Side and Solve
To simplify the right side, your equation will involve a root: 32^(2/5) = (5th root of 32)^2 = 2^2 = 4. With x on the left side and 4 on the right, you have your answer: x = 4.
Check Your Answer
To check your answer, check that x^(5/2) = 32, solving for x = 4. To do this, plug 4 in for x: 4^(5/2) = (square root of 4)^5 = 32.