# Thread: Equations with variables and exponents

1. ## Equations with variables and exponents

In the equation:

(2n^3)^4 (n^-2)^-1

I work it and get 16n^12-n^2. I am not sure what to do with the "-n^2". Help woulld be greatly appreciated.

2. $\displaystyle (2n^3)^4(n^{-2})^{-1}$

$\displaystyle 2^4n^{3\times 4}n^{-2\times -1}$

Can you finish it from here using simple index laws?

Spoiler:
$\displaystyle 16n^{12}n^{2}$

$\displaystyle 16n^{12+2}$

$\displaystyle 16n^{14}$

3. Originally Posted by mrking
In the equation:

(2n^3)^4 (n^-2)^-1

I work it and get 16n^12-n^2. I am not sure what to do with the "-n^2". Help woulld be greatly appreciated.
First, although it may seem "picky", you don't have an equation here, you have an expression. (It isn't equal to anything.)

What do you want to do with the $\displaystyle n^2$? That is, what are you trying to do with the original expression? Simplify it? $\displaystyle 16n^{12}- n^2$ seems simple enough to me! You could, if you wanted, factor out an "$\displaystyle n^2$". $\displaystyle n^{12}= n^{10}n^2$ so [tex]16n^{12}- n^2= n^2(16n^{10}- 1). If you really wanted to you could factor that further- $\displaystyle 16n^10- 1= (4n^5)^2- 1^2$ is the difference of two squares and can be factored as $\displaystyle (4n^5-1)(4n^5+1)$. whether $\displaystyle n^2(4n^5-1)(4n^5+1)$ is "simpler" than $\displaystyle 16n^{12}- n^2$ is a matter of taste or, perhaps better, of what you wanted to do with it from here.

4. Originally Posted by HallsofIvy
First, although it may seem "picky",
You talking to me Halls?

5. I'm going to slide right out of that one!

6. Hmmm....I get a simple 16n^14 ; where does the - come from?

7. Originally Posted by Wilmer
Hmmm....I get a simple 16n^14 ; where does the - come from?
I think there is general confusion around what the equation is and how it is presented.

8. Originally Posted by pickslides
I think there is general confusion around what the equation is and how it is presented.
It's not an equation

9. Its an expression, thanks smarty pants!