I am dealing with Radicals and Complex Numbers. What do I use for this?

Question

The directions say: Evaluate the expression.

1) -12 ^ -2

Would I put a 1 over the -12 and make the exponent of -2 posative 2?
As in:
1/(-12)^2

If I am correct with that, can I go one step further and make the fraction 1/(-144)?

Answer 1

Okay, so the best way to do this is to extract -1s where appropriate. This equivalent expression is:

(-1)*12^((-1)*2)

So, let's deal with that -1 in the exponent first (we could do the 2 first as well, but we gotta start somewhere).

A number to the -1 is an instruction to take everything in the number and flip it (including any other exponents) under the fraction bar.

(-1)*12^((-1)*2) = 1/((-1)*12^2)

Now, the second exponent is an instruction to square the number, and you're right 12^2 = 144 so...

1/((-1)*12^2)=1/((-1)*144), and the -1 can be taken to the numerator:

= -1/144

Okay. So, there are no complex numbers here, just so you know. The only way for that to happen is for the negative sign to be inside an exponent which is less than one.

Hope this helps.

Answer 2

You have it right
-12 ^ -2= - 1/(12^2)= - 1/144

Answer 3

you are correct, up until the (1/(-144))

(-12)^2 = 144, not -144, so the actual answer, should be

1/144

Answer 4

-12^-2
1/-12^2
1/144

Answer 5

you have the right idea. technically, though, if the - sign is not within the parintheses, the final answer will be negative. If the negative sign is within them, the answer will be positive because it's an even exponent. But, you have the right idea.