Question

How do you simplify `\frac { - 2n ^ { 2} } { - 4n ^ { - 4} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(-2/-4)(n^2/n^-4) =>`

`(2/4)(n^2/n^-4) =>`

`1/2(n^2/n^-4)`

Now, use this rule of exponents to simplify the `n` term:

`x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))`

`1/2(n^color(red)(2)/n^color(blue)(-4) =>`

`1/2n^(color(red)(2)-color(blue)(-4)) =>`

`1/2n^(color(red)(2)+color(blue)(4)) =>`

`1/2n^6`

Or

`n^6/2`

Answer 2

`n^6/2 " or " 1/2n^6`

Explanation:

Recall one of the laws of indices which deals with negative indices:

`x^-m = 1/x^m" "and" "1/x^-n = x^n`

This means you can make a factor which has a negative index positive by moving it to the denominator or numerator.

`(-2n^2)/(-4color(blue)(n^-4)) = (-2n^2 xx color(blue)(n^4))/(-4)`

Now simplify as usual.

`(-cancel2n^2 xx n^4)/(-cancel4^2)" "larr` divide the signs, divide the numbers

`= +(n^2xx n^4)/2" "larr` add the indices of like bases

`=+n^6/2`

You could also write this as `1/2n^6`