### Instruction: $P$ and $Q$ represent numbers, and $P \ast Q$ means $\cfrac{P+Q}{2}$. What is the value of $3 \ast (6 \ast 8)$?### Response: This problem involves a non-standard operation, so I need to be careful not to confuse it with regular multiplication.
I can start by simplifying the expression inside the parentheses, using the definition of $\ast$.
So, $6 \ast 8$ means $\cfrac{6+8}{2}$, which is $7$.
Now I have $3 \ast 7$, which means $\cfrac{3+7}{2}$.
That is $5$.
So the value of the expression is $5$.