8filltheheart Posted May 5, 2010 Share Posted May 5, 2010 (edited) I posted this under Linda's thread, but thought I would post here in case people weren't continuing to follow that thread: I thought about it and realized that maybe you don't even understand why any number (other than 0) raised to the 0 power = 1. It all has to do with how exponents operate. I will explain it via a simplified proof. When you multiply numbers with the same base that have exponents, you can see that you add the exponents. x^2 * x^3=x^5 (you should see that by x*x=x^2 and x*x*x=x^3, and therefore altogether: x*x*x*x*x or x^(2+3), so that is the same thing as X^(5) When dividing by same bases with exponents, you subtract the denominator's exponent from the numerator's: x^2/x^3 is the same thing as x*x/x*x*x you should be able to see that you can eliminate the 2 x's in the numerator, leaving 1 x in the denominator which = 1/x. That is the same as x^(2-3) or x^(-1)......a negative exponent indicates an inverse of the number so in this case the number, x, moves to the denominator or 1/x. So, now to prove that any number (other than 0) to the 0 power is 1. x^6/x^6........you should be able to see that the x's are all divisible by each other, thereby leaving you with 1. (similar to 2/2, or 6/6, or 10/10) So, by the rules of exponents that I already explained, x^6/x^6 is the same thing as saying x^(6-6) or x^0. Therefore, it = 1. I hope that helps someone! Edited May 5, 2010 by 8FillTheHeart Quote Link to comment Share on other sites More sharing options...

Violet Crown Posted May 5, 2010 Share Posted May 5, 2010 x^6/x^6........you should be able to see that the x's are all divisible by each other, thereby leaving you with 1. (similar to 2/2, or 6/6, or 10/10) So, by the rules of exponents that I already explained, x^6/x^6 is the same thing as saying x^(6-6) or x^0. Therefore, it = 1. ... and your explanation also demonstrates why 0 to the zeroth power is undefined, rather than being 1. If x = 0, then (x^n)/(x^n) would be 0/0, and any number divided by zero is undefined. Yay math! Quote Link to comment Share on other sites More sharing options...

LizzyBee Posted May 5, 2010 Share Posted May 5, 2010 ... and your explanation also demonstrates why 0 to the zeroth power is undefined, rather than being 1. If x = 0, then (x^n)/(x^n) would be 0/0, and any number divided by zero is undefined. Yay math! I've been watching the Teaching Company Basic Math course with my 8th grader, and we learned that 0/0 is actually indeterminate rather than undefined. The reason is that the quotient can be any number because any number * 0 = 0. If I knew that sometime in the past, I had forgotten it until this week. :tongue_smilie: Quote Link to comment Share on other sites More sharing options...

Violet Crown Posted May 5, 2010 Share Posted May 5, 2010 D'oh! :blushing: You're right. Quote Link to comment Share on other sites More sharing options...

johnandtinagilbert Posted May 5, 2010 Share Posted May 5, 2010 I posted this under Linda's thread, but thought I would post here in case people weren't continuing to follow that thread: I thought about it and realized that maybe you don't even understand why any number (other than 0) raised to the 0 power = 1. It all has to do with how exponents operate. I will explain it via a simplified proof. When you multiply numbers with the same base that have exponents, you can see that you add the exponents. x^2 * x^3=x^5 (you should see that by x*x=x^2 and x*x*x=x^3, and therefore altogether: x*x*x*x*x or x^(2+3), so that is the same thing as X^(5) When dividing by same bases with exponents, you subtract the denominator's exponent from the numerator's: x^2/x^3 is the same thing as x*x/x*x*x you should be able to see that you can eliminate the 2 x's in the numerator, leaving 1 x in the denominator which = 1/x. That is the same as x^(2-3) or x^(-1)......a negative exponent indicates an inverse of the number so in this case the number, x, moves to the denominator or 1/x. So, now to prove that any number (other than 0) to the 0 power is 1. x^6/x^6........you should be able to see that the x's are all divisible by each other, thereby leaving you with 1. (similar to 2/2, or 6/6, or 10/10) So, by the rules of exponents that I already explained, x^6/x^6 is the same thing as saying x^(6-6) or x^0. Therefore, it = 1. I hope that helps someone! I just want to say how happy I am you are here. What a blessing you are...as a whole...to this board. Quote Link to comment Share on other sites More sharing options...

Capt_Uhura Posted May 5, 2010 Share Posted May 5, 2010 :iagree: with johnandtinagilbert! Quote Link to comment Share on other sites More sharing options...

MIch elle Posted May 5, 2010 Share Posted May 5, 2010 http://khanexercises.appspot.com/video?v=8htcZca0JIA It's under "Pre-algebra" here: http://www.khanacademy.org/ Quote Link to comment Share on other sites More sharing options...

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