I need to understand why it's always equal to one, except for the fact it's one of the laws of exponents, and I would need some illustrations (e.g. 6 (raised to zero) = 1)
2006-09-12 01:29:35 · 4 answers · asked by Carmela B 1 in Education & Reference ➔ Homework Help
x^0 essentially means you're not multiplying x at all. Thus, if you're not multiplying anything, you're left with the multiplicative identity - which is 1.
2006-09-12 01:41:32 · answer #1 · answered by ³√carthagebrujah 6 · 1⤊ 0⤋
Well, for one thing, it allows for simpler multiplication of powers.
For example, you probably know 6^3 X 6^2 = 6^(3+2) = 6^5
If we want that to hold for the 'zero power' case then we want
6^3 X 6^0 = 6^(3+0) = 6^3
You can re-arrange that and 'solve' for 6^0
6^3 X 6^0 = 6^3 implies 6^0 = 6^3/6^3 = 1
Generally speaking, a^x X a^y = a(x+y) only holds for all x and y if a^0 = 1.
If you prefer to look at 'patterns', consider the pattern 6^2, 6^1, 6^0, 6^-1
These numbers are: 36, 6, 1, 1/6.
Notice each number in the series is the prior number divided by 6.
2006-09-12 08:36:56 · answer #2 · answered by kheserthorpe 7 · 2⤊ 0⤋
Another way to look at the problem is this:
(a^3)/(a^2) = (aaa)/(aa) Cancel out 2 of the a's, you get a. So 3-2 (the powers of the exponents) equals 1.
So let's look at it this wat: (a^3)/(a^3) = (aaa) / (aaa). Any number divided by itself is 1. Thus, subtracting the exponents, 3-3 = 0. Therefore, any number raised to a zero power equals 1.
2006-09-12 08:49:11 · answer #3 · answered by mthtchr05 5 · 0⤊ 0⤋
e.g. "One is the loneliest number." Except for zero.
2006-09-12 08:33:00 · answer #4 · answered by bereftcat 4 · 0⤊ 0⤋