Question

(2x9y^n)(4x2y10)=8x11y20

Answer 1

$(2x^9y^n)(4x^2y^{10})=8x^{11}y^{20}\\\\(2\cdot4)(x^9\cdot x^2)(y^n\cdot y^{10})=8x^{11}y^{20}\\\\8x^{9+2}y^{n+10}=8x^{11}y^{20}\\\\8x^{11}y^{n+10}=8x^{11}y^{20}\Rightarrow n+10=20\ \ \ |-10\\\\\boxed{n=10}$

$\text{Used:}\\a^n\cdot a^m=a^{n+m}$