1. **State the problem:** Simplify the expression $\left(\frac{4^2}{2^2} + 3^2\right) \div 13 + \left(5^2 - 2^4 - 5\right)^2 - 3^2$. 2. **Calculate powers:** - $4^2 = 16$ - $2^2 = 4$ - $3^2 = 9$ - $5^2 = 25$ - $2^4 = 16$ 3. **Simplify inside the parentheses:** - $\frac{4^2}{2^2} = \frac{16}{4} = \cancel{\frac{16}{4}}{4}$ - So, $\frac{4^2}{2^2} + 3^2 = 4 + 9 = 13$ 4. **Divide by 13:** - $\left(4 + 9\right) \div 13 = 13 \div 13 = \cancel{\frac{13}{13}}{1}$ 5. **Simplify the second parentheses:** - $5^2 - 2^4 - 5 = 25 - 16 - 5 = 9 - 5 = 4$ 6. **Square the result:** - $4^2 = 16$ 7. **Subtract $3^2$:** - $16 - 9 = 7$ 8. **Add the two parts:** - $1 + 7 = 8$ **Final answer:** $8$