Find the term free of x in the expansion of (x³ - 1/2x²)¹⁰. Give its term number and its value.

Step 1. The power of $x$. $T_{r+1} = {}^{10}C_r\,x^{3(10-r)}\left(-\dfrac{1}{2}\right)^r x^{-2r}$, so the power is $30 - 5r$.

Step 2. Solve. $30 - 5r = 0$ gives $r = 6$, so it is the $7$th term.

Step 3. The value. ${}^{10}C_6 \times \left(-\dfrac{1}{2}\right)^6 = 210 \times \dfrac{1}{64} = \dfrac{105}{32} = 3.28125$.