Certainly! Let's break down the expression \( 2 + 8 \cdot (5 - 7)^2 \) step by step, following the proper order of operations:
1. Parentheses: The first step is to evaluate the expression inside the parentheses.
[tex]\[
5 - 7 = -2
\][/tex]
2. Exponentiation: Next, we need to raise the result of the parentheses to the power of 2.
[tex]\[
(-2)^2 = 4
\][/tex]
3. Multiplication: Now, we multiply this result by 8.
[tex]\[
8 \cdot 4 = 32
\][/tex]
4. Addition: Finally, we add 2 to this product.
[tex]\[
2 + 32 = 34
\][/tex]
Therefore, the answer to the expression [tex]\( 2 + 8 \cdot (5 - 7)^2 \)[/tex] is [tex]\( \boxed{34} \)[/tex].
