Question

How do you simplify `\frac { 3u v ^ { - 4} } { 2u ^ { - 1} }`?

Answer 1

See the entire solution process below:

Explanation:

First, use this rule of exponents to rewrite the numerator:

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

`(3u^color(red)(1)v^-4)/(2u^-1)`

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

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

`(3u^color(red)(1)v^-4)/(2u^color(blue)(-1)) = (3u^(color(red)(1)-color(blue)(-1))v^-4)/2= (3u^(color(red)(1)+color(blue)(1))v^-4)/2 = (3u^2v^-4)/2`

Now, use this rule of exponents to eliminate the negative exponent:

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

`(3u^2v^color(red)(-4))/2 = (3u^2)/(2v^color(red)(- -4)) = (3u^2)/(2v^color(red)(4))`