Sure, let's solve the expression step-by-step:
Expression:
[tex]\[ 40 \div [20 - 4 \cdot (7 - 4)] \][/tex]
1. First, we need to solve the parentheses inside the bracket:
[tex]\[ 7 - 4 = 3 \][/tex]
So, the expression now is:
[tex]\[ 40 \div [20 - 4 \cdot 3] \][/tex]
2. Next, perform the multiplication inside the bracket:
[tex]\[ 4 \cdot 3 = 12 \][/tex]
So, the expression now is:
[tex]\[ 40 \div [20 - 12] \][/tex]
3. Now, perform the subtraction inside the bracket:
[tex]\[ 20 - 12 = 8 \][/tex]
So, the expression now is:
[tex]\[ 40 \div 8 \][/tex]
4. Finally, perform the division:
[tex]\[ 40 \div 8 = 5 \][/tex]
Thus, the value of the expression is:
[tex]\[ \boxed{5.0} \][/tex]
