https://file.aiquickdraw.com/mathbot/file/1725902556587ksqyn2nh.jpg

Let's solve the two problems in the image.

### 1. \( 4 + (3 \times 2) + 2^2 \)
We apply the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

- First, calculate \( 3 \times 2 = 6 \).
- Then, calculate \( 2^2 = 4 \).
- Now, the expression becomes \( 4 + 6 + 4 \).
- Finally, add them together: \( 4 + 6 + 4 = 14 \).

So, the answer to the first problem is \( \boxed{14} \).

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### 2. \( 16 - (4 \times 3) + 3^3 \)
Again, applying the order of operations:

- First, calculate \( 4 \times 3 = 12 \).
- Then, calculate \( 3^3 = 27 \).
- Now, the expression becomes \( 16 - 12 + 27 \).
- Perform the subtraction and addition: \( 16 - 12 = 4 \), and \( 4 + 27 = 31 \).

So, the answer to the second problem is \( \boxed{31} \).

Would you like any further details or clarifications?

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Here are 5 related questions to expand on this topic:

1. What happens if you change the exponent in the first equation to \( 2^3 \) instead of \( 2^2 \)?
2. How would the second problem change if you used \( 4 \times 2 \) instead of \( 4 \times 3 \)?
3. Can you solve a problem like \( 5 + (2 \times 3^2) + 4 \)?
4. What is the difference between evaluating exponents and performing multiplication first?
5. How do the rules of parentheses affect the outcome of complex expressions?

**Tip:** Always follow the correct order of operations (PEMDAS) to avoid mistakes in calculations.

1. 4 + (3 × 2) + 2^2 = ?
2. 16 − (4 × 3) + 3^3 = ?

Learn how to solve expressions using the order of operations (PEMDAS). This guide walks through the solutions for 4 + (3 × 2) + 2^2 and 16 − (4 × 3) + 3^3, focusing on exponents and arithmetic rules, suitable for Grades 6-8.

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