Definition: An exponent tells how many times a base is used as a factor in repeated multiplication, so 4<sup>3</sup> means 4 x 4 x 4 = 64.
What is an exponent?
An exponent is the small raised number that says how many copies of the base to multiply together. In 54, the base is 5 and the exponent is 4, so 54 = 5 x 5 x 5 x 5 = 625.
What are the special cases?
- Any number to the power 1 is itself: 91 = 9.
- Squared means exponent 2, and cubed means exponent 3.
- Any nonzero number to the power 0 equals 1.
How do you read powers of ten?
Powers of 10 are easy: 103 = 1,000 and 106 = 1,000,000. The exponent counts the zeros.
What is the biggest error?
Multiplying the base by the exponent. The value of 34 is 3 x 3 x 3 x 3 = 81, not 3 x 4 = 12. Another trap involves negatives: (-2)4 = 16, but -24 = -16, because the exponent applies only to the 2 when there are no parentheses.
Example: 27 = 2 x 2 x 2 x 2 x 2 x 2 x 2 = 128.