Miss Sherry Posted February 16, 2009 Share Posted February 16, 2009 I can't see this. Can someone tell me why any number to the power of zero equals 1 ? It seems like it should equal zero. Thanks, Sherry Quote Link to comment Share on other sites More sharing options...
Snickerdoodle Posted February 16, 2009 Share Posted February 16, 2009 (edited) scroll down a little on this link to the pink shaded box http://www.mathsisfun.com/algebra/exponent-laws.html Also check down to the bottom of that page. Edited February 16, 2009 by Snickerdoodle Quote Link to comment Share on other sites More sharing options...
Dana Posted February 16, 2009 Share Posted February 16, 2009 You can also see that a^0 has to be one for other exponential rules to work. For instance, a^m * a^n = a^(m+n) So if you have 5^3 * 5^6 = 5^9 Now if you had 5^2 * 5^0 = 5^(2+0) = 5^2. The only thing you can multiply 5^2 by to get itself is 1. Therefore for the product rule to stay correct, we have to define a^0 = 1. (Note only true if a isn't 0.) Quote Link to comment Share on other sites More sharing options...
daybreaking Posted February 16, 2009 Share Posted February 16, 2009 (edited) I've also seen it explained: 10^5 = 1 with 5 zeros, thus 100,000 10^4 = 1 with 4 zeros, thus 10,000 10^3 = 1 with 3 zeros, thus 1,000 10^2 = 1 with 2 zeros, thus 100 10^1 = 1 with 1 zero, thus 10 10^0 = 1 with 0 zeros, thus 1 and also this way: 3^5 means 3 times itself 5 times 3^4 means 3 times itself 4 times 3^3 means 3 times itself 3 times 3^2 means 3 times itself 2 times 3^1 means 3 times itself 1 time 3^0 means 3 times itself 0 times, which "by default" or simply "by definition" is 1 Edited February 16, 2009 by daybreaking to correct a typo Quote Link to comment Share on other sites More sharing options...
Miss Sherry Posted February 16, 2009 Author Share Posted February 16, 2009 I can see that 10^0 is 1 but it still doesn't make sense in my mind that all other numbers to the power of zero = 1. I see that Dana said it makes other exponential equations work so I will just have to keep it memorized for now. Thank you for all of your answers. Sherry Quote Link to comment Share on other sites More sharing options...
nmoira Posted February 16, 2009 Share Posted February 16, 2009 I can see that 10^0 is 1 but it still doesn't make sense in my mind that all other numbers to the power of zero = 1. I see that Dana said it makes other exponential equations work so I will just have to keep it memorized for now. 5^4 = 5^3 * 5 5^3 = 5^2 * 5 5^2 = 5^1 * 5 5^1 = 5^0 * 5 5^0 = 5^-1 * 5 which is: (1/5 * 5) = 1 5^-1 = 5^-2 * 5 which is: (1/25 * 5) = 1/5 etc. Quote Link to comment Share on other sites More sharing options...
daybreaking Posted February 16, 2009 Share Posted February 16, 2009 I just found this on answers.yahoo.com: 1 = xⁿ/xⁿ = x^(n - n) = x^0 Quote Link to comment Share on other sites More sharing options...
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