Define 0 and negative exponents
So far we have discussed only positive exponents. Now we define 0 as an exponent. Suppose
we multiply 42by 40. By the product rule, extended to whole numbers,
42 . 40 = 42+0 = 42.
For the product rule to hold true, 40must equal 1, and so we define a0this
way for any nonzero real number a.
If a is any nonzero real number, then
The expression 00is undefined.*
For any natural number n and any nonzero real number a,
a-n = 1/an.