To solve the expression \( 72:8 \ast 7 - (45:9 + 3 \ast 3:2) \), I'll break it down step by step.
Calculate \( 72:8 \): \[ 72 \div 8 = 9 \]
Now calculate \( 9 \ast 7 \): \[ 9 \ast 7 = 63 \]
Next, calculate \( 45:9 \): \[ 45 \div 9 = 5 \]
Now, calculate \( 3 \ast 3 \): \[ 3 \ast 3 = 9 \]
Now, calculate \( 9:2 \): \[ 9 \div 2 = 4.5 \]
Combine the results of \( 5 \) and \( 4.5 \): \[ 5 + 4.5 = 9.5 \]
Now, complete the expression by subtracting \( 9.5 \) from \( 63 \): \[ 63 - 9.5 = 53.5 \]
So, the final result is: \[ \boxed{53.5} \]