How Can a Number Raised to the Zero Power Be One?Date: 01/23/2008 at 14:22:19 From: Aron Subject: WHY is any number raised to a power of zero, one I understand that 3 raised to the 7th multiplied by 3 raised to the 0 is equal to 3 raised to the 7th, because the rule is that you would add the exponents which would give you 3 to the 7th which clearly alludes to the fact that 3 to the zero equals one so that 3 to the 7th is equal to itself........but WHY? How, mathematically is 3 to the zero equal to one???? Date: 01/23/2008 at 15:02:24 From: Doctor Peterson Subject: Re: WHY is any number raised to a power of zero, one Hi, Aron. Our FAQ page has several explanations: N to 0 power http://mathforum.org/dr.math/faq/faq.number.to.0power.html Here is another way to make sense of it: Rather than think of x^n (that is, x raised to the nth power) as x^n = x * x * ... * x \_____________/ n copies of x we can think of it as starting with 1 and then doing n multiplications--literally "multiplying by x, n times" x^n = 1 * x * x * ... * x \_______________/ n multiplications by x Taking it this way, we have: x^2 = 1 * x * x \_____/ 2 multiplications x^1 = 1 * x \_/ 1 multiplication x^0 = 1 \/ 0 multiplications So x^0 is 1, for any x. If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ Date: 01/23/2008 at 15:36:44 From: Aron Subject: Thank you (WHY is any number raised to a power of zero, one) Thank you - your answer is awesome! Aron |
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