any number by the power of nought is one.....im not having this...as anything multiplied by zero is zero...?

Answer 1

More like something common divided by itself is one.
Ex. a/a=1, a^4/a^4 = 1 = a^(4-4) = a^0 . For more details, see http://mathforum.org/dr.math/faq/faq.number.to.0power.html

Answer 2

But remember that for any nonzero number a and any power n of that number, a^n / a = a^(n-1) If we want this very useful property to hold for any power, then surely it's clear that a^0 = a^1/a = a/a = 1 You're correct that a^n is some starting number, multiplied n times by a. But that starting number is one. If the starting number were zero, then a^n would equal zero no matter what value of n you used, and exponentiation would be the same thing as multiplication by zero and we'd have to invent exponentiation all over again (in which case a^0 would still be equal to 1 for any nonzero a). There's room for a bit of quibbling over the case of 0^0, because an attempt to reach a definition using limits hits a difficulty.

Answer 3

Indices (Powers) aer the number of times somethig is multiplied by itself, so 4^1 = 4; 4^2 = 4x4 = 16; 4^3 = 4x4x4 = 64 etc. However, Indices can also be negative, so 4^-1 = 1/4; 4^-1 = 1/(4x4) = 1/16 and they can also be fractions. x^(1/2) = Square Root x etc.
To raise something by power 0 is not the same as multiplying by 0. Anything^0 =1. It's a mathamatical rule, and asking why is like asking why 2+2 =4. It doesn't matter whether you are having it or not. It just is.

Except Migelito up there has given the proof which I could't remember. Nice one mate! Give him 10 points.

Answer 4

im going to explain it in a way that you understand, because even i dont understand what all these other people have written.

If a certain number is to the power of another, then this other sumber (the second one) is how many times you multiply the first number by itself.

If i had 10 to the power of 5, the answer would be: 10x10x10x10x10.

Therefore if i had 10 to the power of 0, it wouldn't have to be multiplied by ANYTHINg!

Answer 5

To raise a number to the power zero is not the same as multiplying it by zero.

using the law of indices, (n^x)*(n^y) = n^(x+y)
so if y = -x, then (n^x)*(n^y) becomes (n^x)/(n^x) and n^(x+y) becomes n^0
Now (n^x)/(n^x) = 1
and so n^0 = 1

Answer 6

Do you understand laws of indices?
Raising to a given power, whatever it is, is not the same as multiplying by that given number
i.e. 4 squared does not equal 4 multiplied by 2

Answer 7

thecharleslloyd:
"I left school 23 years ago and it's all very dull in my memory. But if i have 10 of some thing and i multiply it by 0 i would still have 10. Are we talking roulette. Forgive me here to learn."

No you wouldnt still have 10. think of it as "lots of" lol, if u have 1 lots of 10, u have 10. so 10x1= 10.
if you have 0 lots of 10, you have nothing, so 10x0 = 0.


I cant even be bothered to answer the actual question. its already been done.


now lets prance. like children of the night!

Answer 8

The common exponentiation definition that is used to explain this is that a^n = 1 * a * ... * a. Using this identity element of multiplication we can clearly see that:

a^0 = 1
a^1 = 1 * a
a ^ 2 = 1 * a * a
...

Answer 9

I left school 23 years ago and it's all very dull in my memory. But if i have 10 of some thing and i multiply it by 0 i would still have 10. Are we talking roulette. Forgive me here to learn.

Answer 10

Maegical is absolutely correct. But just remember that a cannot be zero because 0/0 is **not** 1, it is undefined ☺


Doug