The value of this expression ((-27/8)^(n/3)), n=2,4,5,7,8,... can be worked out manually, but why is it that the calculator cannot evaluate this expression? Is it because of the programming / algorithms used by a general scientific calculator? Or is it because the expression cannot be worked out manually? Is the topic of complex numbers involved?
2007-02-05 19:17:14 · 3 answers · asked by mathematics problematic 1 in Science & Mathematics ➔ Mathematics
The value of this expression ((-27/8)^(n/3)), n=2,4,5,7,8,... can be worked out manually, but why is it that the calculator cannot evaluate this expression? Is it because of the programming / algorithms used by a general scientific calculator? Or is it because the expression cannot be worked out manually? Is the topic of complex numbers involved? However, the calculator can evaluate the expression when n=1,3,6,... Why is this so, when other values of n, when n is not equals to 1 or to a multiple of 3, cannot be evaluated?
2007-02-07 11:53:58 · update #1
I would expect the calculator works out general non-integral powers by using the formula a^b = exp (b ln a), and therefore has problems when a is negative.
However, this is not necessarily true for there to be significant problems with trying to compute these powers.
Note that (n/3) cannot be represented exactly in binary, so the actual power it is trying to compute will be some binary fraction approximating n/3. As such, in complex numbers the answer is likely to be a complex number whose real part "coincidentally" is close to 0. However, unless your calculator has been programmed to calculate complex logs and exponentials (and I'm not aware of any that do), it cannot calculate it on this basis.
Note that in the reals, we can only take rational powers of negative numbers if the denominator in reduced form is odd. In a calculator, every non-integer number is a fraction where the denominator is a power of 2. So it's no surprise that the calculator can't evaluate expressions like this.
2007-02-05 19:36:18 · answer #1 · answered by Scarlet Manuka 7 · 2⤊ 0⤋
It works on Ti-graphing calculaters. Just pretend [n = x], insert the function, push the graph button, and you will have the graph. Click trace, and type in your numbers (x=2,4,5,7,8,...) and you will get the corresponding values.
2007-02-06 03:22:28 · answer #2 · answered by Phillip R 4 · 2⤊ 0⤋
it's the negative inside the root that messes it up
2007-02-13 22:42:29 · answer #3 · answered by erselius 3 · 0⤊ 0⤋