Question

How do you divide `\frac { 6x ^ { 3} y ^ { 2} } { 8x ^ { 4} y ^ { 5} } \div \frac { 2x } { 12x y ^ { 2} }` ?

Answer 1

`(9)/(2xy)`

Re-write into multiplication format, multiply together like terms, divide away like terms on the numerator and denominator.

Explanation:

Dividing something by a fraction is the same as multiplying that same 'something' by the inverse of the fraction (swap the denominator and numerator locations).

`(6x^3y^2)/(8x^4y^5) * (12xy^2)/(2x)`

From here, multiply like terms together.

`(72x^4y^4)/(16x^5y^5)`

Divide like terms away.

`(9)/(2xy)`

This can be done because `x^5` and `y^5` can be re-written as `x^4 * x` and `y^4 * y` respectively. Thus, the variable being raised to the fourth on both the numerator and denominator effectively cancels each other out, leaving you with just one `x` and one `y` on the denominator of the end result.