How do you simplify \frac { 65x ^ { 2} x ^ { 11} y ^ { 5} y ^ { 9} } { 5x x ^ { 3} y ^ { 2} x ^ { 2} }?

Mar 24, 2018

$13 {x}^{7} {y}^{2}$

Explanation:

$\frac{65 {x}^{2} {x}^{11} {y}^{5} {y}^{9}}{5 x {x}^{3} {y}^{2} {x}^{2}} \rightarrow$ Combine all the like terms in the numerator and the denominator first

$\frac{65 {x}^{2 + 11} {y}^{5 + 9}}{5 {x}^{1 + 3 + 2} {y}^{2}}$

$\frac{65 {x}^{13} {y}^{14}}{5 {x}^{6} {y}^{2}}$

65 is evenly divisible by 5

$\frac{13 {x}^{13} {y}^{14}}{{x}^{6} {y}^{2}} \rightarrow$ Exponents can be subtracted from each other when dividing (ex. ${x}^{6} / {x}^{2} = {x}^{6 - 2} = {x}^{4}$)

$13 {x}^{13 - 6} {y}^{14 - 2}$

$13 {x}^{7} {y}^{2}$