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Powers with negative exponents

Definition of powers with negative exponents

a real number a, different from zero, raised to a negative integer -m is equal to a fraction where the numerator is equal to 1 and the denominator is equal to a raised to the positive number m:
a-m = 1/am

Note that the exponent -m is an integer.

Example:

2-3 = 1/23 = 1/8

Examples of powers with negative exponents

Power with a negative exponent:

5-3 = 1/53 = 1/125

A power with a negative exponent:

12-3 = 1/123

A negative base with a negative exponent:

(-5)-3 = 1/(-5)3 = -1/125

An expression with a negative exponent:

(a + b)-3 =
1/(a + b)3

A power with a negative exponent:

53/55 =
5(3 - 5) =
5-2 =
1/52 =
1/25