# How do you simplify 4.98^0?

Jan 20, 2017

${4.98}^{0} = \textcolor{g r e e n}{1}$

#### Explanation:

Any number (excluding perhaps zero) to the power of $0$ is equal to $1$

Consider the following sequence for any number $n$ which is not zero:

$\textcolor{w h i t e}{\text{XXX}} {n}^{4} = n \times n \times n \times n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{3} = \frac{{n}^{4}}{n} = n \times n \times n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{2} = \frac{{n}^{3}}{n} = n \times n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{1} = \frac{{n}^{2}}{n} = n$

$\textcolor{w h i t e}{\text{XXX}} {n}^{0} = \frac{{n}^{1}}{n} = \frac{n}{n} = 1$

...and we could continue on:

$\textcolor{w h i t e}{\text{XXX}} {n}^{- 1} = \frac{{n}^{0}}{n} = \frac{1}{n}$

$\textcolor{w h i t e}{\text{XXX}} {n}^{- 2} = \frac{{n}^{- 1}}{n} = \frac{1}{{n}^{2}}$

$\textcolor{w h i t e}{\text{XXX}} {n}^{- 3} = \frac{{n}^{- 2}}{n} = \frac{1}{{n}^{3}}$

...and so on...

Jan 20, 2017

Another way of writing ${4.98}^{0}$ is : $\frac{4.98}{4.98} = 1$