Negative Integer Exponents MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts

Exponents can be represented as positive integers, negative integers, or zero.
See Exponent Basics for more information on positive integer exponents (or zero).

 Negative Integer Exponents

The use of a negative integer exponent has special meaning and a rule explaining its use.

 For any non-zero number x, and for any positive integer n,

The use of a positive exponent is an application of repeated multiplication by the base:
43 = 4 • 4 • 4 = 64.
The use of a negative exponent produces the opposite of repeated multiplication.
It can be thought of as a form of repeated division by the base:
4-3 = 1 ÷ 4 ÷ 4 ÷ 4 = 0.015625

Examples:

 1.       Notice: making x-1 the reciprocal of x. 2. 3. 4. 5. 6. 7.

 For calculator help with exponents click here.

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