I REALLY need the answer for this because for my test question, there was this question that said,
"Give a convincing arguement that 3 to the power of 0 is 1 using the fact that 3 to the power of 4 is 81, 3 to the power of 3 is 27, 3 to the power of 2 is 9, and 3 to the power of 1 is 3."
2007-01-19 13:30:40 · 14 answers · asked by Spectrum 1 in Science & Mathematics ➔ Mathematics
when we lower the power that '3' is being raised to, the result is divided by 3
2007-01-19 13:34:04 · answer #1 · answered by Anonymous · 1⤊ 0⤋
The power of 0 is the number itself. 3/3 = 1.
2007-01-19 13:35:39 · answer #2 · answered by Anonymous · 0⤊ 0⤋
3^4 / 3^3 = 81/27 = 3
3^3 / 3^2 = 27/9 = 3
3^2/ 3^1 = 9/3 = 3
3^1 / 3^0 = 3
3^0 = 3^1 / 3 = 3/3 = 1
2007-01-19 14:13:41 · answer #3 · answered by Northstar 7 · 0⤊ 0⤋
What is 3 to the power of -1 or 3 to the power of -2? Both of these are less than one. All positive powers of 3 are greater than one. Therefore, 3 to the power of zero cannot be greater than or less than one and by limit theory is one as the function 3 to the x power approaches the value one as you take the limit with x approaching 0 from both the positive and negative sides. It is more than convention, it is necessary for 3 to a negative power to be a number less than one that 3 to the zero power is one.
However, I do like this three divided by itself arguement. It is basically the same thing that I am saying only more simple.
2007-01-19 13:35:23 · answer #4 · answered by msi_cord 7 · 0⤊ 0⤋
Because it is actually translated as multiplying itself by it's reciprocal.
3 to the power zero is 3 x 1/3.
3 to the power 1 is 3 x 3/3=3
3 to the power 2 is 3 x (3x3)/3=9
etc.
2007-01-19 13:40:26 · answer #5 · answered by bigdonut72 4 · 0⤊ 0⤋
1^0 = 1. It's no different than any other number.
2016-05-23 23:15:51 · answer #6 · answered by Anonymous · 0⤊ 0⤋
You can say that as each power is lowered, the previous power is divided by 3 to get the next lowest power. This is an argument based on the facts above, but it is not the reason anything to the zero power is 1. That is by definition.
Bozo
2007-01-19 13:35:52 · answer #7 · answered by bozo 4 · 1⤊ 0⤋
A real answer is:
think of the pattern.
2 ^3=8
2^2=4
2^1=2
2^0=1
notice that each time the right of the equation is halved. thats why. its just following the pattern
2007-01-19 13:40:07 · answer #8 · answered by teenhaunt 2 · 1⤊ 0⤋
use the law of exponents for division
so 3^4/3^1=3^(4-1)
81/3=27=3^3
so 3^3/3^1=3^(3-1)
27/3=9=3^2
so 3^2/3^1=3^(3-1)
9/3=3=3^1
so 3^1/3^1=3^(1-1)=3^0
so 3^0=1
2007-01-19 13:38:35 · answer #9 · answered by dla68 4 · 0⤊ 0⤋
Expressing a number to the power 0 is the same as saying the number divided by itself - so it will always be 1 whatever the number.
It's just a mathematical expression, that's how it is.
2007-01-19 13:36:12 · answer #10 · answered by Trevor 7 · 1⤊ 0⤋