Home >> Science & Nature >> Science

How to Calculate With a Power That Is a Negative Exponent

Exponents denote how many times a number or variable, called the base, should be multiplied by itself. For example, 3^3 equals 3 * 3 * 3 and x^4 equals x * x * x * x. Another way to phrase x^4 would be to say it is "x to the power of four." Exponents can be integers, fractions or variables. There can also be negative exponents, which follow rules of their own.

Instructions

- 1
  Simplify or solve a negative exponent using the negative exponent rule, which states that x^-a = 1 / (x^a) or, if the problem begins as an inverse, 1 / (x^-a) = x^a.
- 2
  Simplify and add 3^-2 + (1 / (2^-2)). Write the first exponential term in the form of an inverse to eliminate the negative exponent: 3^-2 = (1 / (3^2)). Write the second term out of inverse form to eliminate the negative exponent: (1 / (2^-2)) = 2^2. Rewrite the addition problem: (1 / (3^2)) + 2^2.
- 3
  Simplify by applying the exponents: (1/9) + 4. Convert the 4 to fractional form with a common denominator to perform the addition: (1/9) + (36 / 9) = (37 / 9) or 4.1 (rounded).

Science