Question

How do you divide `(24x^2y^2) / (14x^3y^7)`?

Answer 1

`(24x^2y^2)/(14x^3y^7) = 12/(7xy^5)`

Explanation:

`(24x^2y^2)/(14x^3y^7)`

`color(white)("XXXX")` `=color(red)((24/14)) * color(blue)(((x^2)/(x^3))) * color(green)(((y^2)/(y^7)))`

`color(white)("XXXX")` `= color(red)((12/7)) * color(blue)((1/x)) * color(green)((1/y^5))`

`color(white)("XXXX")` `= 12/(7xy^5)`

Answer 2

Simplify `24/14` to `12/7` by dividing by `2`. Apply the quotient rule and negative power rule of exponents.

Explanation:

`(24x^2y^2)/(14x^3y^7)`

Divide the numerator and denominator by `2`.

`(12x^2y^2)/(7x^3y^7)`

Apply the exponent quotient rule: `x^a/x^b=x^a-b`.

`(12x^(2-3)y^(2-7))/(7)` =

`(12x^(-1)y^(-5))/(7)` =

Apply the exponent negative power rule: `x^-a=1/x^a`.

`12/(7x^1y^5)` =

`12/(7xy^5)`