How to Multiply With a Negative Exponent


As you advance in your algebra studies, you will begin to work with exponents. Exponents are the equivalent of multiplying a number by itself a certain number of times. The proper way to multiply negative exponents is a bit misleading because according to the laws of math, you must actually perform division to get your answer. By rewriting the equation using division, the negative exponent falls away, and the equation can be solved.

  • Learn how to rewrite the equation. Each piece of the equation with a negative exponent will need to be rewritten so that the exponent becomes positive. This is done by placing the exponential term in the denominator of an equation with the number "1" placed in the numerator:

    x^-n = 1/(x^n)

    "X" represents the number and "N" represents the exponent.

  • Rewrite the equation you wish to solve. For example, if your problem was 4^-3 x 5^-2 = Y. The equation would be rewritten as:

    Y = 1 /(4^3) x 1/(5^2)

    In this equation, "Y" represents the value for which you are solving.

  • Multiply the exponents on each side of the equation. Therefore:

    4^3 (or 4 x 4 x 4) = 64 and 5^2 (or 5 x 5) = 25.

    Rewrite the equation as Y = 1/64 x 1/25

  • Multiply the denominators on each side of the equation. Using a calculator can save you time from longhand multiplication. The example would compute as the following:

    Y = 1/64 x 1/25

    64 x 25 = 1,600

    Rewrite the equation given your new answer. Y = 1/1,600

  • Solve for "Y" to obtain your answer. Again a calculator can save you from longhand division.

    Y = 1/1600

    Y = 0.000625

Tips & Warnings

  • "X" can never equal 0 in this equation.
  • If you have an equation that multiplies exponents that have the same base, you can simply add the exponents when simplifying.


  • Photo Credit Jupiterimages/ Images
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