# How do you simplify 2^ 0?

Feb 29, 2016

${2}^{0} = 1$

#### Explanation:

For any non-zero number $a$:

${a}^{0} = 1$

Note that ${0}^{0}$ is undefined, except in restricted circumstances.

$\textcolor{w h i t e}{}$
Here's one way of thinking of it:

If $n$ is a positive integer, then:

$2 \cdot n = {\overbrace{2 + 2 + \ldots + 2}}^{n \textcolor{w h i t e}{x} \text{times}}$

When $n = 0$ then $2 \cdot n$ is an empty sum, with value $0$, the identity under addition.

${2}^{n} = {\overbrace{2 \times 2 \times \ldots \times 2}}^{n \textcolor{w h i t e}{x} \text{times}}$

When $n = 0$ then ${2}^{n}$ is an empty product, with value $1$, the identity under multiplication.

Feb 29, 2016

anything powered zero is equal to one

Feb 29, 2016

1

#### Explanation:

Think in:
${2}^{1} / {2}^{1} = 1$

Because we know that a number divided by itself is 1.

And as you may already know, when you divide exponents you just subtract them.
To simplify:
${2}^{1 - 1} = 1$
${2}^{0} = 1$

There is also a pattern:
${2}^{3} = 8$
${2}^{2} = 4$
${2}^{1} = 2$
Same base, decrease the exponent by 1 and get half the value
so:
${2}^{0} = 1$