Sure, let's solve the expression [tex]\(9+6\left(2^2+4\right)\)[/tex] step-by-step using the order of operations, often remembered by the acronym PEMDAS: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
1. Parentheses first:
Evaluate the expression inside the parentheses [tex]\((2^2+4)\)[/tex].
- Exponents: Evaluate [tex]\(2^2\)[/tex]. This results in [tex]\(4\)[/tex].
- Now the expression inside the parentheses is [tex]\(4+4\)[/tex].
2. Addition inside the parentheses:
- Evaluate [tex]\(4+4\)[/tex]. This results in [tex]\(8\)[/tex].
- So the expression simplifies to [tex]\(9 + 6 \cdot 8\)[/tex].
3. Multiplication:
- Evaluate [tex]\(6 \cdot 8\)[/tex]. This results in [tex]\(48\)[/tex].
4. Addition:
- Evaluate [tex]\(9 + 48\)[/tex]. This results in [tex]\(57\)[/tex].
Therefore, the final answer is:
[tex]\[
9 + 6\left(2^2 + 4\right) = 57
\][/tex]
