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# 1 and -1 to different powers

Different exponents affect the value of a number: when raised to the power of zero, any number equals one; when raised to an even power, negative numbers yield positive results; and when raised to an odd power, negative numbers yield negative results. Created by Sal Khan.

## Want to join the conversation?

• plz try to explain it as if you were explaining this to a small kid plz that might help me
• I think Sal making the video longer is what's confusing us! But it's actually pretty simple! One to the power of ANY NUMBER will always be one because you just keep on doing 1 x 1 x 1 x 1 etc. When you do -1 to the power of an ODD number, the answer is always -1, but when you do -1 to the power of an even number, the result is always just 1! :) Let me know if this helps!
• At how does 1^0 equal 1?
• Anything to the 0 power is equal to 1 unless you do 0^0.
• Why is 2^0 equal to one?
• Any non-zero number to the power of 0 is always equal to one. Here's a way I like to think about it:

You have 8x^2 apples, 7x^1 apples, 6x^1 apples and 5 apples. Now, since the 5 apples have no 'x' variable inside, you can express that term as 5x^0. If x^0 was 0, then 5 x 0 would be 0, and the 5 apples would just disappear. For this to mathematically work, you could only make x^0 (x=non-zero number) equal to 1!
• Is zero an even or odd power?
• 0 is an even number and is hence an even power.
• After a few days do you gt use to doig it
• yes you would surely get used to it
(1 vote)
• Is (-1)^infinity an indeterminate form? Or was it just 1^infinity that was an indeterminate form... because ln(-1) when we try and take the limit of it is undefined. So (-1)^k as k approaches infinity diverges?
A series from K=0 to infinty of (-1)^k diverges because (-1)^infinty is infinity because it is not an indeterminate form? I am pretty lost how this diverges...I'm trying to learn properties of power series.
• 0 is an even number and is hence an even power.
• Isn't it easier to do the math without the 1 at ?