Whole Number Exponents with Integer Bases

b^x = b . b . b . b …… b.

b appears as a factor x times

Can the base of an exponent be negative?

The base of an exponent may be negative also. If the exponent is an even integer with a negative base, then the resulting value will be positive as it gets multiplied even number of times.

If the exponent is an odd integer with a negative base, then the resulting value will be negative as it gets multiplied an odd number of times.

Let’s see the rules for whole-number exponents with integer bases.

Rules for whole number exponents with integer bases

Example: Solve (-4)³

(-4)³ = -4 × -4 × -4 = -64

Example: Solve (-3)⁴

(-3)⁴ = -3 × -3 × -3 × -3 = 81

Check Point

Simplify the following:

1. (2)⁵
2. (-5)⁴
3. (4)⁵
4. (-7)³
5. (-9)⁴

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