Question

How do you simplify `\frac { 4n ^ { 4} \cdot 2n } { 3m ^ { 4} n ^ { 2} \cdot 2m ^ { 3} n ^ { 3} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(4 * 2)/(3 * 2)(1/(m^4 * m^3))((n^4 * n)/(n^2 * n^3)) =>`

`(4 * color(red)(cancel(color(black)(2))))/(3 * color(red)(cancel(color(black)(2))))(1/(m^4 * m^3))((n^4 * n)/(n^2 * n^3)) =>`

`4/3(1/(m^4 * m^3))((n^4 * n)/(n^2 * n^3))`

Next, use this rule of exponents to rewrite the `n` terms:

`a = a^color(blue)(1)`

`4/3(1/(m^4 * m^3))((n^4 * n^color(blue)(1))/(n^2 * n^3))`

Now, use this rule of exponents to simplify each of the numerators and denominators:

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

`4/3(1/(m^color(red)(4) * m^color(blue)(3)))((n^color(red)(4) * n^color(blue)(1))/(n^color(red)(2) * n^color(blue)(3))) =>`

`4/3(1/(m^(color(red)(4)+color(blue)(3))))((n^(color(red)(4)+color(blue)(1)))/(n^(color(red)(2)+color(blue)(3)))) =>`

`4/3(1/m^7)(n^5/n^5) =>`

`4/3(1/m^7)(color(red)(cancel(color(black)(n^5)))/color(red)(cancel(color(black)(n^5)))) =>`

`4/(3m^7)`