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

1 Answer
Dec 1, 2016

#(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.