We can evaluate the expression step by step. The expression is:

\[
3 \left[ 4 + (5 + 3) \times 2 \right]^2
\]

### Step 1: Simplify inside the parentheses

\[
5 + 3 = 8
\]

Now the expression becomes:

\[
3 \left[ 4 + 8 \times 2 \right]^2
\]

### Step 2: Multiply \(8 \times 2\)

\[
8 \times 2 = 16
\]

Now the expression is:

\[
3 \left[ 4 + 16 \right]^2
\]

### Step 3: Add \(4 + 16\)

\[
4 + 16 = 20
\]

Now the expression is:

\[
3 \times 20^2
\]

### Step 4: Square 20

\[
20^2 = 400
\]

Now the expression becomes:

\[
3 \times 400
\]

### Step 5: Multiply \(3 \times 400\)

\[
3 \times 400 = 1200
\]

### Final Answer:

The value of the expression is \(1200\).

Would you like more details or have any questions? Here are some related questions to explore:

1. How would the result change if the constant "2" inside the expression were different?
2. How do parentheses affect the evaluation of mathematical expressions?
3. What is the effect of changing the exponent in similar expressions?
4. How can we use distributive properties in simplifying expressions like this?
5. What are the common mistakes made when dealing with order of operations?

**Tip**: Always follow the order of operations—parentheses, exponents, multiplication/division, addition/subtraction (PEMDAS).

Learn how to evaluate the expression 3[4 + (5 + 3)2]^2 using the order of operations (PEMDAS). This step-by-step guide covers simplifying exponents, multiplication, and addition, providing a clear understanding of how to solve such expressions. Ideal for Grades 7-8 students.

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