Find the constant term in the expansion of $$\left(10x^3-\frac{1}{2x^2}\right)^{5}$$
That's true. We can see that $a=2$ and $b=3$. That means that the constant term will be $\binom{5}{2}(10x^3)^{2}\left(-\frac{1}{2x^2}\right)^{3}$. Right, so we just need to evaluate that expression. We know that $\binom{5}{2}=10$. Also, $(10x^3)^{2}=100x^6$. Finally, $\left(-\frac{1}{2x^2}\right)^{3}=\frac{-1}{8x^6}$. So, we just need to calculate $10\cdot 100x^6 \cdot \frac{-1}{8x^6}$. That is equal to $-\frac{1000}{8}=-125$. Finally, we can see that the constant term is $-125$.

