How do you simplify $2^{0}$ $2^ 0$ ?

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Answer 1 · 2016-02-29T19:05:48

$2^{0} = 1$ $2^0 = 1$

For any non-zero number $a$ $a$ :

$a^{0} = 1$ $a^0 = 1$

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

$color(white)()$
Here's one way of thinking of it:

If $n$ $n$ is a positive integer, then:

$2*n = overbrace(2+2+...+2)^(n color(white)(x)"times")$

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

$2^n = overbrace(2xx2xx...xx2)^(n color(white)(x)"times")$

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

Answer 2 · 2016-02-29T19:07:36

anything powered zero is equal to one

Answer 3 · 2016-02-29T19:15:27

1

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:
$2^0=1$

How do you simplify 2^ 0202^ 0?