Why is it 1?
how is it that 0 to the power of 2 or to the power
of any number equals 1?????
TB simply sent us this website:
David K sent us an explanation:
Actually, you got it backwards! The
number ZERO to any power is ZERO (because 0 multiplied by anything
is ZERO), but any number to the power of zero is one. Then you may
ask, what's zero to the power of zero then? It seems like a paradox.
One way to think about this is to look at the following
x^1 = x^2 / x = x^(2-1)= x
x^0 = x^1 / x^1 = x^(1-1) = 1
Now if you substitute "0" in place of "x" in the 2nd equation, you
have a problem because you end up with "0" in the denominator, and
we all know that is an "undefined" value.
I think 0^0 is undefined, yet my calculator says it's "1". Go
MyHeadHurts replied with this:
Not strictly true, I'm afraid. 0
to the power anything but 0 equals 0, and 0 to the power 0 equals (I
think) 1, as does anything else to the power 0 (definitely). As to
why this is, my math teacher told me once but I cant remember for
the life of me...
pavolka sang to us this answer:
Simple. One is the loneliest number that you'll ever
Keith helped out with this:
Actually, 0 to the power of anything is
undefined (like dividing by zero - any attempt at a definition leads
to a contradiction).
On the other hand, any number (except 0) to the power of 0 is 1. Any
number (except 0) to the power of 1 is the number. So 10^1 is 10 and
10^0 is 1.
C.H.U.D. faithfully replied with this:
It's not. Zero to any power is zero, not one.
Curt responded with this:
it is simply a mathematical term in
which any number raised to the power of zero, except zero, equals
one. It is a mathematical rule that applies to make sense so just
deal with it.
Mr. Obvious stated this:
0 to the power of 2 does not equal 1. It equals 0.
Pull up your computer's calculator and try it.
Paul concluded with this:
Zero to any power does not equal one, rather it is
the other way around. Any number raised to the power of zero equals
A number raised to the power of 2 is that number multiplied by
itself twice (2^2 = 2x2). The exponent indicates how many times a
number is multiplied by itself (2^3 = 2x2x2). A number raised to a
negative exponent indicates the inverse (2^-2 = 1/2*2).
The exponent zero indicates that the number is divided by itself,
which always equals 1.
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