# Exponents with fractions and - sign

1. Aug 26, 2011

### ttttrigg3r

what does this simplify to: (-33/2)2/3

I use the exponent rules to multiply the fractions to get (-31) which comes out to -3, but the answer key says the real answer is 3. Is there something important when doing fractional exponent that I'm missing out? Thanks in advance.

2. Aug 26, 2011

### HallsofIvy

Staff Emeritus
$\left(-3^{3/2}\right)^{2/3}=$$((-3^{3/2})^2)^{1/3}$
Does that clarify it?

Another way to look at it is that $(-3^{3/2})^{2/3}=$$(-1)^{2/3}(3^{(3/2)(2/3)})$. $(-1)^{2/3}= 1$, not -1.

Last edited: Aug 26, 2011
3. Aug 26, 2011

### Ray Vickson

Use of the "rules of exponents" is NOT recommended when you have fractional powers of negative quantities. If you interpret your quantity as A = [(-3)^(3/2)]^(2/3), using the laws of exponents gives A = (-3)^1 = -3. However, the actual value (using general definitions in terms of functions in the complex plane) is A = (3/2) - I*(3/2)*sqrt(3), where I = sqrt(-1). On the other hand, if you meant to write B = [-(3^(3/2)]^(2/3), the laws of exponents gives B = (-1)^(2/3)*3 = (-1)^2*3 = 3. However, the actual value is B = -(3/2) + I*(3/2)*sqrt(3).

RGV

4. Aug 26, 2011

### Staff: Mentor

I don't believe this is a correct interpretation of the problem. The OP shows it as -33/2, not (-3)3/2.
This is probably overkill in the context in which this problem was posed (as a prealgebra problem). I believe HallsOfIvy's approach is the right way to go, although it appears that he omitted a factor of 3 towards the end of his calculation.

Corrected, it would be (−33/2)2/3=(−1)2/3(3(3/2)(2/3)) = 1 * 3 = 3

Last edited: Aug 26, 2011
5. Aug 26, 2011

### ttttrigg3r

(−33/2)2/3=((−33/2)2)1/3 That I got but (−33/2)2/3=(−1)2/3(3(3/2)(2/3)). (−1)2/3 . 3 = 3 this i do not get. Why is there a multiplication factor there?

side note. how do you copy and paste while keeping super and subscripts?

6. Aug 26, 2011

### Staff: Mentor

Because -3 = -1 * 3. That's really all that's going on for that part.
You can't. I had to reproduce the superscripts from what I had copied.

7. Aug 26, 2011

### ttttrigg3r

(−33/2)2/3=(−1)2/3(3(3/2)(2/3)). (−1)2/3 . 3

looking at that equation, I understand that -3 is the same thing as -1*3 and so that is where (−1)2/3(3(3/2)(2/3)) came from but the additional (−1)2/3 . 3 after that I don't get. where did that last part come from? is the first . supposed to be a multiplication sign or a period? if it is a period it would make sense.

sidenote:
is (x-1/3)/(y-1/3)=(y1/3)/(x1/3)

Last edited: Aug 26, 2011
8. Aug 26, 2011

### Staff: Mentor

You're right - it shouldn't be there. I copied from HallsOfIvy's post and didn't notice that extra stuff. I corrected it in my earlier post. The expression in HTML is quite complicated, with all those SUP and /SUP tags, so I can see that it would be easy to forget to put something in, which is what I believe happened. Sorry for adding to the confusion.
The period is meant to indicate multiplication. I changed it to * to make that clearer.
Yes.

9. Aug 26, 2011

### ttttrigg3r

Ah then it is perfectly clear. Thanks for the help.

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