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 $\boxed{14}$.

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?

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.