# Equations with variables and exponents

• Nov 7th 2010, 11:13 AM
mrking
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.
• Nov 7th 2010, 12:00 PM
pickslides
$(2n^3)^4(n^{-2})^{-1}$

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

Can you finish it from here using simple index laws?

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

$16n^{12+2}$

$16n^{14}$
• Nov 7th 2010, 12:05 PM
HallsofIvy
Quote:

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 $n^2$? That is, what are you trying to do with the original expression? Simplify it? $16n^{12}- n^2$ seems simple enough to me! You could, if you wanted, factor out an " $n^2$". $n^{12}= n^{10}n^2$ so [tex]16n^{12}- n^2= n^2(16n^{10}- 1). If you really wanted to you could factor that further- $16n^10- 1= (4n^5)^2- 1^2$ is the difference of two squares and can be factored as $(4n^5-1)(4n^5+1)$. whether $n^2(4n^5-1)(4n^5+1)$ is "simpler" than $16n^{12}- n^2$ is a matter of taste or, perhaps better, of what you wanted to do with it from here.
• Nov 7th 2010, 12:11 PM
pickslides
Quote:

Originally Posted by HallsofIvy
First, although it may seem "picky",

You talking to me Halls? (Rofl)(Nod)
• Nov 7th 2010, 12:30 PM
HallsofIvy
I'm going to slide right out of that one!
• Nov 7th 2010, 12:52 PM
Wilmer
Hmmm....I get a simple 16n^14 ; where does the - come from?
• Nov 7th 2010, 12:54 PM
pickslides
Quote:

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.
• Nov 7th 2010, 03:56 PM
Wilmer
Quote:

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 :)
• Nov 7th 2010, 03:58 PM
pickslides
Its an expression, thanks smarty pants!