Let's solve each of the equations from the image:

Problem 13

$1^2 + 2^2 + 3^2 + 4^2 = 1 + 4 + 9 + 16 = 30$ Answer: 30

Problem 14

$3^3 \div 9 + 128 \div 4^2$ Calculate each part:

• $3^3 = 27$ and $27 \div 9 = 3$
• $4^2 = 16$ and $128 \div 16 = 8$ $3 + 8 = 11$ Answer: 11

Problem 15

$(5 + 1)^2 + 107$ Calculate each part:

• $5 + 1 = 6$ and $6^2 = 36$ $36 + 107 = 143$ Answer: 143

Problem 16

$\frac{63}{3^2} + 5^3 - 4^2$ Calculate each part:

• $3^2 = 9$ and $63 \div 9 = 7$
• $5^3 = 125$
• $4^2 = 16$ $7 + 125 - 16 = 116$ Answer: 116

Problem 17

$2(40 + 21 \cdot 6) - 10^2$ Calculate each part:

• $21 \cdot 6 = 126$
• $40 + 126 = 166$
• $2 \cdot 166 = 332$
• $10^2 = 100$ $332 - 100 = 232$ Answer: 232

Problem 18

$(9^2 + 8^2) - 144 \div 12$ Calculate each part:

• $9^2 = 81$ and $8^2 = 64$
• $81 + 64 = 145$
• $144 \div 12 = 12$ $145 - 12 = 133$ Answer: 133

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Would you like further details on any of these solutions, or have additional questions?

Here are five related questions to extend your understanding:

1. What is the general formula for calculating the sum of squares?
2. How does exponentiation impact order of operations in a complex expression?
3. How can you simplify expressions that involve both division and exponents?
4. What steps can help avoid errors in multi-step arithmetic problems?
5. How does the distributive property apply in equations like Problem 17?

Tip: Always follow the order of operations (PEMDAS/BODMAS) to ensure accurate results.