Question

How do you simplify `\frac { x ^ { 2} y ^ { - 3} } { 3y ^ { 2} } \cdot \frac { y ^ { 2} } { x - 4}`?

Answer 1

See a solution process below:

Explanation:

First, cancel common terms in the numerator and denominator and multiply:

`(x^2y^-3)/(3y^2) * y^2/(x - 4) =>`

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

`(x^2y^-3)/(3(x - 4))`

Next. use this rule of exponents to eliminate the negative exponent:

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

`(x^2y^color(red)(-3))/(3(x - 4)) =>`

`x^2/(3y^color(red)(- -3)(x - 4)) =>`

`x^2/(3y^3(x - 4))`

If necessary, we can expand the denominator as:

`x^2/((3y^3 xx x) - (3y^3 xx 4)) =>`

`x^2/(3xy^3 - 12y^3)`