Simplify & eliminate negative exponents

[Janinever]

Hi there,

Please help :) out of school for years started studying again and finding it so hard to pick up the basics again! But am trying very hard!

Homework Statement

Simplify the expression and eliminate any negative exponents

Homework Equations

(2x^3)^-2 (3x^4)^2
----------------------
(3x)^2

The Attempt at a Solution

I'm given a list of options to choose from as an answer which is :
(a) 1/4x^5
(b) 2x^6
(c) 4x^12
(d) None of the above


I'm chosen none of the above because from a very crooked attempt at getting to an answer I got 4x as being the answer.

Please help :) No clue if I'm right or wrong.

Thank you!

 

[Robert1986]

Well, None of the above is right, but 4x isn't.

Show some more work. In particular, why do you think the answer is 4x?

 

[Janinever]

Hi there! Thanks for replying! I have one more problem - the rest I did without trouble but first I'll show you what I did (this coming week I'll have time off to properly cover the basics because it sucks wanting to do this but not being able to!).

(2x^3)^-2 (3x^4)^2
----------------------
(3x)^2

= (4x^-6)(9x^8) 36x^2
---------------- = ------------ = 4x (I attempted to get to some sort of answer...)the last problem I honestly have no clue I've tried numerous things substituting the values into the equation but not sure what I'm suppose to be getting.
I'm doing a distance learning course and the textbook just doesn't have enough info, really pathetic.

--The real solution(s) of the equation 2x - (sqrt 11x+23) +5 = 0

Options are:
(a) x=7, x=-2
(b) x=-2
(c) x=-1/4 , x=-2
(d) No real solution

I know I sound like such an idiot :) But this is a difficult task for me being out of school for 10 years almost - but will be doing everything in my power to succeed & appreciate any and all help very, very much!

Thanks again!

 

[NewtonianAlch]

Is your ---------- meant to be a division sign?

 

[Janinever]

yes :)

 

[Robert1986]

Well, I think that to go from the original problem to $(4x^{-6})(9x^8)$ you are probably making some arithmetic errors when adding exponents and such. The $9x^8$ is right. Now, thing about the $\frac{(2x^3)^{-2}}{(3x)^2}$. What, exactly, do negative exponents mean? (And, on a side note, let's try think about WHY they might mean that.)

For the second one, first, try to do something about the square root sign.

 

[NewtonianAlch]

When you get negative indices like this:

(2x^3)^-2

Consider turning it into its fractional form so in reality, the equation turns into:

$\frac{(3*x^4)^2}{((2*x^3)^2*(3*x)^2)}$

Can you do it now?