Hey,
I am working with a TI-89 calculator, on this problem:
(−27)^2/3
So this is what I did. I know that (x^a)^b = x^(ab), so I didn't think that the order of the exponents mattered.
First try: (-27^1/3)^2 = -3^2
At -3^2 I could type this into my calculator, or I could type -3*-3.
-3^2 = -9 but -3*-3 = 9
Second try (I ran into the same kind of problem): (-27^2)^1/3
-27^2 = -729 but -27*-27 = 729
I'm pretty sure that two negatives multiplied equals a positive, but what is my calculator doing? I would greatly appreciate anyone's help!
It is definitely wrong!. When squaring a negative number, it should give you a positive answer. Even when raising ANY negative integer to an ODD integer, it should give you a negative answer. Just to get around these problems, you might consider removing the - from the number, and see if it will give the expected answer, and then place the - sign in front of the answer, manually.
I'm not familiar with TI-89 calculator. But you should know that most calculators will not allow you to raise a negative number to any fraction, because (-27)^2/3=(-27^2)^1/3=-729^1/3, which means you are taking the 3rd root of negative number, which most calculators cannot do. Taking any root of a negative number is considered a "complex operation", which involves square root of -1 or i. In fact, the answer to your question is=9 (-1)^(2/3), in complex operation.
(reply)
I didn't realize that. But it is the only way I can find the square cube (raising the number to the 1/3), because my calculator doesn't have a cube root button. This calculator is also pretty old, so I don't know if it changes anything, but thanks for the input!
But am I right in thinking that it's doing something wierd when I square a negative number and I get another negative number? (That was my original question)
It is definitely wrong!. When squaring a negative number, it should give you a positive answer. Even when raising ANY negative integer to an ODD integer, it should give you a negative answer. Just to get around these problems, you might consider removing the - from the number, and see if it will give the expected answer, and then place the - sign in front of the answer, manually.
+118608 (-27^1/3)^2 = -3^2
Taking fractional powers of negative numbers often causes problems for calculators.
(Often it really does not makes sence for people either. Though a good example escapes me at present.)
Even new and fancy calcs have problems.
I am sure some people here understand and can explain it a lot better than me.
\((27^{2/3})\\ =(27^2)^{1/3}=729^{1/3}=9\\ =(27^{1/3})^2=3^2=9\\\)
\((-27)^{2/3} \\ ((-27)^2)^{1/3}=729^{1/3}=+9\\ ((-27)^{1/3})^2=(-3)^2=+9\)
I do not agree with something the first guest said. This statement is inaccurate because brackets have been left out.
(-27)^2/3=(-27^2)^1/3=-729^1/3,
It should be
(-27)^2/3=([-27]^2)^1/3=+729^1/3 = +9
