Question

How do you simplify `\frac { u v } { 4u v ^ { 2} }`?

Answer 1

See a solution process below:

Explanation:

First, cancel common terms in the numerator and denominator:

`(uv)/(4uv^2) => (color(red)(cancel(color(black)(u)))v)/(4color(red)(cancel(color(black)(u)))v^2) => v/(4v^2)`

Next, use these rules of exponents to complete the simplification:

`a = a^color(red)(1)` and `x^color(red)(a)/x^color(blue)(b) = 1/x^(color(blue)(b)-color(red)(a))` and `a^color(red)(1) = a`

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