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# I need help

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Why is it that if you put 2^0 you would get 1?

Guest Jun 3, 2017
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#1
+4154
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Any number, except for zero, raised to the power of zero equals 1 .

Here is one way of thinking about why this is. I've never heard it explained like this, but I really like his explanation! I will probably think of it this way from now on!

And....I was trying to find a good video explaining it another way, but I couldn't really find a good one. Here's a pretty good answer to your question that you can read through if you want.

http://mathforum.org/dr.math/faq/faq.number.to.0power.html

hectictar  Jun 3, 2017
edited by hectictar  Jun 3, 2017
#2
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I think I have an explanation that is simple to understand! In advance, I have not referenced any of Hecticlar's sources before writing this explanation, so mine could be similar or different. To start, I am going to make a table of powers that we can calculate:

 $$2^n$$ Written-out Result $$2^5$$ 2*2*2*2*2 32 $$2^4$$ 2*2*2*2 16 $$2^3$$ 2*2*2 8 $$2^2$$ 2*2 4 $$2^1$$ 2 2 $$2^0$$ ? ? $$2^{-1}$$ 1/(2) 1/2 $$2^{-2}$$ 1/(2*2) 1/4 $$2^{-3}$$ 1/(2*2*2) 1/8 $$2^{-4}$$ 1/(2*2*2*2) 1/16 $$2^{-5}$$ 1/(2*2*2*2*2) 1/32

Do you notice a pattern? I do. As you go down the list, you can divide by 2 to get the next number in the sequence! FIrst, I'll generalize this statement:

$$\frac{2^n}{2}=2^{n-1}$$

What I have done here is manipulate the powers so that I can circumvent raising to the power of 0. If I make n=1, I will raise to the power of zero and get a result of what that answer should be. Let's try it!

 $$\frac{2^1}{2}=2^{1-1}$$ Let's simplify the right hand side first by doing 1-1 $$\frac{2^1}{2}=2^0$$ Woah! Evaluate the left hand side to figure out what 2^0 truly equals. $$\frac{2}{2}=2^0$$ $$1=2^0$$

We can generalize this further to say that any number raised to the power of zero is 1 using some algebra:

 $$1=\frac{x^n}{x^n}\hspace{1mm},x\neq0$$ This statement is true because any number divided by itself is one! I'll use an exponent rule that says that $$\frac{x^n}{x^n}=x^{n-n}$$ $$1=x^{n-n}$$ n-n=0, so let's simplify that $$1=x^0\hspace{1mm},x\neq0$$ This is saying that any number to the power of zero is one.
TheXSquaredFactor  Jun 3, 2017
#3
+1148
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Guest, there's 1 basic rule. Anything to the power of 0, is one. So, $$2^0$$=1

tertre  Jun 3, 2017

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