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+5
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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!

Guest Oct 26, 2015

Best Answer 

 #4
avatar
+5

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.

Guest Oct 26, 2015
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5+0 Answers

 #1
avatar
+5

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.

Guest Oct 26, 2015
 #2
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+5

(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)

Guest Oct 26, 2015
edited by Guest  Oct 26, 2015
 #3
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0

(?27)^2/3

there

Guest Oct 26, 2015
 #4
avatar
+5
Best Answer

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.

Guest Oct 26, 2015
 #5
avatar+91045 
+5

(-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

Melody  Oct 27, 2015

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