# How do you simplify 9^0?

Sep 9, 2015

${9}^{0} = 1$

#### Explanation:

Anything raised to $0$ is equal to $1$.

To see why, let's first consider how we increase the exponent of a number, by multiplying.

${9}^{1} = 9$
${9}^{2} = 9 \times 9$
${9}^{3} = 9 \times 9 \times 9$
$\ldots$

So, to decrease the exponent of a number, we divide.

${9}^{3} = 9 \times 9 \times 9$

${9}^{2} = \left(9 \times 9 \times 9\right) \div 9 = 9 \times 9$

${9}^{1} = \left(9 \times 9\right) \div 9 = 9$

And if we take it one step further:

${9}^{0} = 9 \div 9 = 1$

We can actually take it even further, and end up with negative exponents.

${9}^{- 1} = 1 \div 9 = \frac{1}{9}$

${9}^{- 2} = \frac{1}{9} \div 9 = \frac{1}{81}$

$\ldots$

So you can see why ${9}^{0} = 1$.