2/3 Power using a Calculator
Date: 07/05/2001 at 11:49:34 From: Tan Jia Hui Subject: Indices Hi, I'm currently facing this particular problem of whether -512 can be the answer to the equation x^(2/3) = 64. When I use my calculator, it simply gives error. Can you explain? Thanks a lot! Regards, Tan Jia Hui
Date: 07/05/2001 at 12:41:10 From: Doctor Peterson Subject: Re: Indices Hi! The problem is that the calculator is not as smart as you and I; it doesn't know any math. It has to convert 2/3 to a decimal before using it, and x^0.66666666 does not exist for a negative number, though x^(2/3) does. Such a power only exists for rational exponents whose denominator is odd, and 0.666666666 doesn't simplify to an odd denominator. Since you know that you want the 2/3 power exactly, you can just square -512 and then take the cube root; or take the cube root of -512 and then square it. In fact, try using your calculator this way: ((-512)^2)^(1/3) or ((-512)^(1/3))^2 Mine can do both of these. I'm not sure how it manages to do the latter; perhaps it recognizes 1/3 as a special case. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/
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