# Zero Exponents

Many beginning students think it's weird that anything raised to the power of $0$ is $1$. (I hear a lot of people say "It should be $0!$") You can use the product of powers property to show why this must be true.

${7}^{0}\times {7}^{1}={7}^{(0+1)}={7}^{1}$

We know ${7}^{1}=7$ . So, this says that ${7}^{0}\times 7=7$ . What number times $7$ equals $7$? If we try $0$, we have $0\times 7=7$ . No good. The only number that works is $1$.

In general, for all real numbers *a*, $a\ne 0$,
we have:

${a}^{0}=1$

Note that ${0}^{0}$
is undefined.
(Click here to see why.)