How to Calculate Powers of Numbers

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The powers of numbers are also called exponents. A number, ​X​, to the power of 2 is also referred to as ​X​ squared. The number ​X​ to the power of 3 is called ​X​ cubed. ​X​ is called the base number. Calculating an exponent is as simple as multiplying the base number by itself.

  1. Work with Positive Exponents and Base Numbers

  2. Learn to work with positive exponents and positive base numbers. The exponent tells you how many times to multiply the number by itself. For instance, three to the power of four, or 34, will be:

    3 × 3 × 3 × 3 = 9 × 9 = 81
  3. Calculate with Negative Exponents

  4. Calculate a negative exponent using inversion. When the exponent is a negative number, you are using the inverse of the number. For example, three to the power of negative four, or 3 −4, will be equal to one over three to the power of positive four

    \frac{1}{3^4} \text{ or } \frac{1}{3 × 3 × 3 × 3} \text{ or } \frac{1}{81}
  5. Look Out for Negative Base Numbers

  6. Use care when calculating a negative base number. When the base number is negative, you must follow the rules of multiplying negative numbers. This means that if the base number is even, the answer will be positive, and if the base is an odd number, the answer will be negative. For instance, negative 2 to the power of 2, or -22 is:

    -2 × -2 = 4

    But negative 2 to the power of 3 is:

    -2 × -2 × -2 = 4 × -2 = -8
  7. Calculate the Number to the Power of 0

  8. By definition, number to the power of 0 will always equal 1.


About the Author

Based in Portland, Ore., Miranda Sinclair has been writing professionally since 2009. She holds a B.A. in English and theater from the University of Oregon, as well as an M.A. in English and certificate in teaching college composition from San Francisco State University. Sinclair works as a tutor and teacher of writing.