Question

How do you multiply and simplify `\frac { ( 4n ^ { - 5} ) ( 10n ^ { 6} ) } { 2n }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`((4 * 10)/2)((n^-5 * n^6)/n) =>`

`(40/2)((n^-5 * n^6)/n) =>`

`20((n^-5 * n^6)/n)`

Now, use these rules of exponents to simplify/multiply the numerator of the `n` term:

`x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))` and `a^color(red)(1) = a`

`20((n^color(red)(-5) * n^color(blue)(6))/n) => 20(n^(color(red)(-5)+color(blue)(6))/n) => 20n^color(red)(1)/n => 20n/n =>`

`20 * 1 => 20`