13.6 Exercise 57

In the expansion of $\left(5 x + 3 y\right)^{n} ,$ each term has the form $\begin{pmatrix} n \\ k \end{pmatrix} a^{n – k} b^{k}$, where $k$ successively takes on the value $0 , 1 , 2 , ... , n .$ If $\begin{pmatrix} n \\ k \end{pmatrix} = \begin{pmatrix} 7 \\ 2 \end{pmatrix} ,$ what is the corresponding term?