Question

How do you multiply and simplify `\frac { 12x ^ { 2} y } { 5y ^ { 2} } * \frac { 2x y } { 3x ^ { 2} }`?

Answer 1

See a solution process below:

Explanation:

First, rewrite this expression as:

`(12 * 2)/(5* 3)((x^2 * x)/x^2)((y * y)/y^2)`

First, we can cancel like terms in the numerators and denominators of the fractions:

`(color(red)(cancel(color(black)(12)))4 * 2)/(5* color(red)(cancel(color(black)(3))))((color(blue)(cancel(color(black)(x^2))) * x)/color(blue)(cancel(color(black)(x^2))))((y * y)/y^2) =>`

`8/5x((y * y)/y^2)`

We can now use these rules of exponents to multiply and simplify the `y` terms:

`a = a^color(red)(1)` and `x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))`

`8/5x((y^color(red)(1) * y^color(blue)(1))/y^2) =>`

`8/5x((y^(color(red)(1)+color(blue)(1)))/y^2) =>`

`8/5x(y^2/y^2) =>`

`8/5x(color(red)(cancel(color(black)(y^2)))/color(red)(cancel(color(black)(y^2)))) =>`

`8/5x`