An exponent is a number that designates the power to raise a number or variable and tells you how many times to use the number or variable as a factor of itself. For example, x^3 equals x as a factor of itself three times, which equals x times x times x. You can calculate the opposite of an exponent by taking the root of a number and its exponent. This will undo the exponent and leave only the number or variable. For example, you can get rid of the exponent in the equation x^3 = 27 to solve for the variable x.
Determine a number or variable with an exponent of which you want to calculate the opposite. For example, calculate the opposite of x^2 in the equation x^2 = 9.
Identify the number of the exponent to determine what root to take of the number and its exponent. For example, the exponent is 2, so you need to take the equal number root to undo the exponent, which is the square root.
Calculate the square root of the number and its exponent to calculate the opposite of the exponent and eliminate the exponent. For example, the square root of x^2 is x because the square root cancels out the exponent of 2.
Calculate the same root of the other side of the equation to balance the equation and solve for the variable. For example, calculate the square root of 9, which equals 3. This leaves x = 3, which is the solution to the equation without the exponent.