If m is a positive integer, a x a x a … m times is written as am. a is called the base and m is the power. The power is also called “the index” or “the exponent”.
Exponentiation is an extension of multiplication, just as multiplication is an extension of addition.
We can think of multiplication as the repeated addition of a number. For example, 3 + 3 + 3 + 3 + 3 = 3 x 5
Similarly, we can consider exponentiation as the repeated multiplication of a number. For example,
3 x 3 x 3 x 3 x 3 = 35
Meaning of am
When m = 0, am = 1 for all .
When m is a positive integer, am = a×a×a×a… m times
When m is a negative integer, say m = -n (where n is positive),
When m is a positive or negative fraction, see examples:
- a1 = a
- 1m = 1
Problems on indices normally involve simplifying the terms or solving an equation to identify an unknown, which could either be a base or a power. In addition to the laws of indices, there are some additional rules that will be useful for simplifying the terms or solving the equation.
Evaluation of exponent forms: