**Define 0 and negative exponents**

** **

** **So far we have discussed only positive exponents. Now we define 0 as an exponent. Suppose

we multiply 4^{2}by 4^{0}. By the product rule, extended to whole numbers,

4^{2} . 4^{0} = 4^{2+0} = 4^{2}.

For the product rule to hold true, 4^{0}must equal 1, and so we define *a*^{0}this

way for any nonzero real number *a*.

**Zero Exponent**

If *a *is any nonzero real number, then

*a*** ^{0}**=

**1.**

*The expression 0*^{0}** is undefined**.*

**Negative Exponent**

For any natural number *n *and any nonzero real number *a*,

a^{-n} = 1/a^{n}.