# How do you simplify 2^0 - 2^-2?

Mar 4, 2018

The result is $\frac{3}{4}$.

#### Explanation:

The definition of a negative exponent is as follows:

$\quad {\textcolor{red}{a}}^{-} \textcolor{b l u e}{x} \quad \implies \quad \frac{1}{\textcolor{red}{a}} ^ \textcolor{b l u e}{x}$

Also, anything to the power of $0$ is $1$, so:

$\quad {\textcolor{b l u e}{a}}^{0} = 1$

Now, let's use these properties to simplify the expression:

$\textcolor{w h i t e}{=} \textcolor{red}{{2}^{0}} - \textcolor{b l u e}{{2}^{-} 2}$

$= \textcolor{red}{1} - \textcolor{b l u e}{{2}^{-} 2}$

$= \textcolor{red}{1} - \textcolor{b l u e}{\frac{1}{2} ^ 2}$

$= \textcolor{red}{1} - \textcolor{b l u e}{\frac{1}{4}}$

$= \textcolor{red}{\frac{4}{4}} - \textcolor{b l u e}{\frac{1}{4}}$

$= \textcolor{p u r p \le}{\frac{3}{4}}$

That's the result. Hope this helped!