Question

How do you simplify `\frac { 7x ^ { 2} y ^ { 6} } { 14x ^ { 2} y ^ { 3} }`?

Answer 1

See a solution process below:

Explanation:

First, cancel common terms in the numerator and denominator:

`(color(red)(cancel(color(black)(7)))1color(blue)(cancel(color(black)(x)))y^6)/(color(red)(cancel(color(black)(7)))2color(blue)(cancel(color(black)(x)))y^3) => y^6/(2y^3)`

Then use this rule for exponents to simplify the `y` term:

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

`y^color(red)(6)/(2y^color(blue)(3)) => y^(color(red)(6)-color(blue)(3))/2 => y^3/2`

Or

`1/2y^3`