https://file.aiquickdraw.com/mathbot/file/1734220337760h8m79bb9.jpg

Let's simplify the given expression step by step:

\[
\frac{8 + 3 \left[ (16 + 2^3) \div 6 + 8 \right]}{2}
\]

### Step 1: Simplify the exponent
\[
2^3 = 8
\]
So, the expression inside the brackets becomes:
\[
(16 + 8) \div 6 + 8
\]

### Step 2: Simplify addition inside the parentheses
\[
16 + 8 = 24
\]
Now the expression is:
\[
24 \div 6 + 8
\]

### Step 3: Perform division
\[
24 \div 6 = 4
\]
Now the expression is:
\[
4 + 8
\]

### Step 4: Simplify addition inside the brackets
\[
4 + 8 = 12
\]
Now the entire expression simplifies to:
\[
\frac{8 + 3(12)}{2}
\]

### Step 5: Multiply
\[
3 \times 12 = 36
\]
So the expression becomes:
\[
\frac{8 + 36}{2}
\]

### Step 6: Simplify addition
\[
8 + 36 = 44
\]
Now the expression is:
\[
\frac{44}{2}
\]

### Step 7: Perform division
\[
44 \div 2 = 22
\]

### Final Answer:
\[
\boxed{22}
\]

---

Would you like me to explain any step in more detail? Here are 5 related questions to expand your understanding:

1. How would the solution change if the exponent were \(2^4\) instead of \(2^3\)?
2. What happens if the division operator is replaced with multiplication in this expression?
3. Can you simplify a similar expression with more nested brackets?
4. How does the order of operations (PEMDAS) affect this calculation?
5. What if the denominator was a different number, like 4 instead of 2?

**Tip:** Always remember to follow the order of operations (PEMDAS/BODMAS) when simplifying expressions.

Simplify the following expression: (8 + 3[(16 + 2^3) ÷ 6 + 8]) ÷ 2

Learn how to simplify the algebraic expression (8 + 3[(16 + 2^3) ÷ 6 + 8]) ÷ 2 step by step using the order of operations (PEMDAS). This problem involves exponents, division, addition, and multiplication, ideal for students in Grades 6-8.

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