3.62: Binomial expansion coefficients

Find the term independent of $x$ in the expansion of $\left(x^{2}-\dfrac{3}{x^{4}}\right)^{15}$.

In the expansion of $(1+ax)^{9}$ the coefficient of $x^{3}$ is $7$ times the coefficient of $x^{2}$. Given that $a$ is a positive constant, find the value of $a$.