I know it's 1, but my dad keeps on saying it's zero. He thinks it's like that cycology thing when they say 1+1=3, because 1 of them split into 2. But I don't think it's like that at all.
I don't know how to explain it but my pre-algebra teacher said it was 1 and a whole bunch of other people but he still thinks it's 0, So if you do know how to explain it, please do.
Any # to the 0th power is 1, right????
2007-11-30 2:10 am
回答 (4)
2007-11-30 2:15 am
✔ 最佳答案
any numer to the zero power is one, except for 0To explain this you have to think about the laws of exponents.
Let me explain.
if you have the fraction 5/5 it equals 1, right?
so if I have n^3 / n^3, it also equals 1
if the numerator and denominator are the same the fraction equals 1.
now the laws of exponents says that when dividing powers you subtract the exponents.
example: n^5 / n^3 = n^2
so for the previous example: n^3 / n^3 = n^0, which we said before is equal to 1
so this shows that any number to the zero power is 1 (except for 0)
參考: 7th grade chapter 3
2007-11-30 2:18 am
I dont know how to explain why it is true that any number to the zeroth power is ONE. BUT i can give you many examples why it has to be true for the whole world to work . JUST to illustrate it, a very fundamental and easy example to follow would be .. .. . .
EG.
you know that x^m / x^n = x^(m-n) from year 9 algebra.
if you were given 2^4 / 2^2 , cancelling 2^2 from top and bottom, you obtain 2^2 / 2^0 , then 2^0 MUST BE ZERO for the answer to be 4/1 =4 which is correct since the Q translates to 16/4 =4.
EG.
you know that x^m / x^n = x^(m-n) from year 9 algebra.
if you were given 2^4 / 2^2 , cancelling 2^2 from top and bottom, you obtain 2^2 / 2^0 , then 2^0 MUST BE ZERO for the answer to be 4/1 =4 which is correct since the Q translates to 16/4 =4.
參考: Myself
2007-11-30 2:13 am
yes its one. In multiplication a number to the 0th power must equal one or else everything will equal zero such as 8*3^0 would equal 8. Its used as identity.
2007-11-30 2:17 am
Yes, any number to the zeroth power is 1, including 0^0.
One way to think about it is to draw a parallel with addition. Suppose you're adding up a bunch of numbers. You start with 0, and then add each number to it in order to accumulate the sum. So the "empty sum", where you don't have any numbers to add, is zero.
The same idea applies with multiplication. If you're multiplying a bunch of numbers together, you start with 1, and then multiply it by the first number, then multiply that by the second number, and so on, to accumulate the entire product. If you don't have any numbers, then all you have is the "empty product", which is 1. Exponentiation is just a special case of this, where the numbers you're multiplying are all the same, but if you don't have any numbers to multiply, the base is irrelevant, so the value is 1 no matter what.
One way to think about it is to draw a parallel with addition. Suppose you're adding up a bunch of numbers. You start with 0, and then add each number to it in order to accumulate the sum. So the "empty sum", where you don't have any numbers to add, is zero.
The same idea applies with multiplication. If you're multiplying a bunch of numbers together, you start with 1, and then multiply it by the first number, then multiply that by the second number, and so on, to accumulate the entire product. If you don't have any numbers, then all you have is the "empty product", which is 1. Exponentiation is just a special case of this, where the numbers you're multiplying are all the same, but if you don't have any numbers to multiply, the base is irrelevant, so the value is 1 no matter what.
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