smc

By the Binomial Theorem, each term of the expansion is $\left(\genfrac{}{}{0ex}{}{7}{n}\right)(a{)}^{7-n}(\frac{-1}{\sqrt{a}}{)}^n$. We want the exponent of $a$ to be $-\frac{1}{2}$, so $$(7-n)-\frac{1}{2}n=-\frac{1}{2}$$ $$-\frac{3}{2}n=-\frac{15}{2}$$ $$n=5$$ If $n=5$, then the corresponding term is $$\left(\genfrac{}{}{0ex}{}{7}{5}\right)(a{)}^2(\frac{-1}{\sqrt{a}}{)}^5$$ $$-21a^{-\frac{1}{2}}$$ The answer is $\boxed{-21}$.