Why does any number to the zero power equal 1?

Question

Answer in complete sentences.

Answer 1

Any number raised to the 0 power equals one because it is the number multiplied by itself 0 times.
EX. a^0=a
b^0=b

Answer 2

You must be knowing that any number divided my itself is 1. Say 2/2 = 1 then .. 3/3 = 1 and so on ..

Now according to the rules of the power, when u want to divide the same number with different power, u substract the power of the denominator frm the power of numerator -

To illustrate this : (8^5)/(8^3) = 8^(5-3) which makes it 8^2 = 64
Now consider a sum like 8/8 - you know the answer's 1
but it can also be expressed as 8^1/8^1 (because any number with power 1 is the number itself !)
So according to the rules - 8^1/8^1 = 8^(1-1) = 8^0 = 1
(because 8/8 = 1)

In this way it applies to any number !

Moreover, any number to the zero power means the number is being divided by itself.

Answer 3

A number raised to the zeroth power does, indeed, seem like a nonsensical equation: However, you need to examine how powers work NEAR 0:

Any number raised to the power of 1 is itself:

x^1 = x

Any number raised to the power of 1/2 is it's square root:

16^1/2 = 4

Any number raised to the power of 1/4 is it's fourth root:

16^1/4 = 2

You can keep doing this for increasingly smaller number in the power:

x^1/a

as a gets larger and larger, you will see that the product approaches closer and closer to 1:

2^1/2 = 1.41
2^1/3 = 1.26
2^1/4 = 1.19
2^1/10 = 1.07
2^1/100 = 1.007
2^1/1000 = 1.0007

If you consider the negative powers, you'll see that as they approach zero from the opposite side they, too, approach the product of the equation being 1. You can see it in this graph of y = 2^x:

http://www.walterzorn.com/grapher/grapher_e.htm

Input into the text box 2^x and you'll see.

The point is, the function:

y = k^x approaches y = 1 as x approaches 0 from both sides, for any value of k except k = 0. Therefore it's considered an axiom that k^0 = 1 for all k except k = 0. k = 0 is a tricky case and the proof of that is a lot longer and more complicated.

Answer 4

8 To The Zero Power

Answer 5

This Site Might Help You.

RE:
Why does any number to the zero power equal 1?
Answer in complete sentences.

Answer 6

It doesn't make sense, right?

But when you raise a number to a power n, it means you are multiplying that number to itself n times. Some mathematicians say that since you are multiplying the number by zero times, and there is only one number, that is why it is equal to 1.

For example, 5^2 means 5x5, or "five squared." 5^3 means 5x5x5, or "five cubed." But for 1^0 = 1

So when you raise 1 to the n times, with n being 0, it only equals one.

A weirder question would be 0^0. Some say it equals one, while others say it is undefined.

Answer 7

MY STUDENTS KEEP ON ASKING ME THAT BUT :
promise to give me best answer CZ it really is :
try to divide 5^3 by 5^3
first way subtract powers :
5^(3-3) = 5^0
we will assume we don't know what 5^0 is
try to use your sense now to solve the same problem
5^3 / 5^3
any number divided it self gives whattttt
1 of course
so the two answers must match
so 5^0 =1
gotcha didn't I
HOPE THAT HELPS

Answer 8

Zero to the power of zero does not equal 1, it equals zero.

But your first answer was good, with the exception of the bad examples.

a^0 = 1 a^1 = a a^2 = aa
b^0 = 1 b^1 = b b^2 = bb

If you graph this, it becomes visually clear why x^0 = 1,
when x ≠ 0

Answer 9

It can be any number. Let the number be n
and therefore, n to the power 0 means
n^(any number - that number)
= n^that number / n^that number
= 1

Answer 10

I don't know exactly why but here's an example:

If you were to do a^2/a^2, in order to divide letters with exponents, you have to subtract the exponents. So, 2-2=0. However, that just means you get rid of the exponents. Your real answer is a. a is the same as saying 1a. Even though it's really a^0, which is the same as a^1.

Answer 11

Because x/x = 1 for all numbers (except 0, in that case we have to tkaethe limit). Any number to the zeroth power is that number divided by itself.