To evaluate the expression [tex]\( 7 + (5 - 9)^2 + 3 \left( \frac{16}{8} \right) \)[/tex], we need to follow the order of operations (PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).
Let's break it down step-by-step:
1. Evaluate inside the parentheses/brackets first:
[tex]\[
5 - 9 = -4
\][/tex]
2. Apply the exponent to the result:
[tex]\[
(-4)^2 = 16
\][/tex]
3. Perform the division inside the parentheses/brackets:
[tex]\[
\frac{16}{8} = 2
\][/tex]
4. Multiply the result by 3:
[tex]\[
3 \times 2 = 6
\][/tex]
5. Add all the results together:
[tex]\[
7 + 16 + 6 = 29
\][/tex]
Therefore, the value of the expression [tex]\( 7 + (5 - 9)^2 + 3 \left( \frac{16}{8} \right) \)[/tex] is [tex]\( \boxed{29} \)[/tex].
