Answer
$${\text{seventh term}} = 2189187{m^8}{n^6}$$
Work Step by Step
$$\eqalign{
& {\text{seventh term of }}{\left( {m - 3n} \right)^{14}} \cr
& {\text{In the seventh term, }} - 3n{\text{ has an exponent of }}7 - 1,{\text{ or 6, }} \cr
& {\text{while }}m{\text{ has an exponent of 14}} - 6,{\text{ or 8}}{\text{.}} \cr
& \cr
& {\text{Using the }}k{\text{th Term of The Binomial Expansion}} \cr
& {\text{seventh term}} = C\left( {14,6} \right){\left( m \right)^8}{\left( { - 3n} \right)^6} \cr
& {\text{seventh term}} = \frac{{14!}}{{8!6!}}\left( {{m^8}} \right)\left( {729{n^6}} \right) \cr
& {\text{seventh term}} = 3003\left( {{m^8}} \right)\left( {729{n^6}} \right) \cr
& {\text{seventh term}} = 2189187{m^8}{n^6} \cr} $$
