Question

How do you simplify `\frac { 5c ^ { 2} } { 15a c }`?

Answer 1

See a solution process below:

Explanation:

First, factor the constants as:

`(5c^2)/(15ac) = (5c^2)/((5 xx 3)ac) = (color(red)(cancel(color(black)(5)))c^2)/((color(red)(cancel(color(black)(5))) xx 3)ac) =`

`c^2/(3ac)`

Now, use these rules for exponents to simplify the `x` terms:

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

`c^color(red)(2)/(3ac^color(blue)(1)) = c^(color(red)(2)-color(blue)(1))/(3a) = c^(color(red)(1))/(3a) = c/(3a)`