Sure, let's evaluate the expression [tex]\( 7 + (5 - 9)^2 + 3(16 \div 8) \)[/tex] step-by-step using the order of operations (PEMDAS/BODMAS):
1. Parentheses: Perform operations inside parentheses first.
[tex]\[ 5 - 9 = -4 \][/tex]
So, the expression now is:
[tex]\[ 7 + (-4)^2 + 3(16 \div 8) \][/tex]
2. Exponents: Next, evaluate the exponent.
[tex]\[ (-4)^2 = 16 \][/tex]
So, the expression now is:
[tex]\[ 7 + 16 + 3(16 \div 8) \][/tex]
3. Division: Perform the division inside the parentheses.
[tex]\[ 16 \div 8 = 2 \][/tex]
So, the expression now is:
[tex]\[ 7 + 16 + 3 \cdot 2 \][/tex]
4. Multiplication: Perform the multiplication.
[tex]\[ 3 \cdot 2 = 6 \][/tex]
So, the expression now is:
[tex]\[ 7 + 16 + 6 \][/tex]
5. Addition: Finally, perform the addition from left to right.
[tex]\[ 7 + 16 = 23 \][/tex]
[tex]\[ 23 + 6 = 29 \][/tex]
Therefore, the value of the expression is [tex]\( \boxed{29} \)[/tex].
