Question

How do you simplify `\frac { 7v ^ { 5} w ^ { 4} } { 28v ^ { 3} w ^ { 3} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(7/28)(v^5/v^3)(w^4/w^3) => 1/4(v^5/v^3)(w^4/w^3)`

Next, use this rule of exponents to divide the variables:

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

`1/4(v^color(red)(5)/v^color(blue)(3))(w^color(red)(4)/w^color(blue)(3)) => 1/4v^(color(red)(5)-color(blue)(3))w^(color(red)(4)-color(blue)(3)) =>`

`1/4v^2w^1`

Now, use this rule of exponents to simplify the `w` variable:

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

`1/4v^2w^color(red)(1) =>`

`1/4v^2w`