\( 74\left[10 \cdot(2 \cdot 5-14: 2)-3^{2}\right]: 3+\left[\left(5 \cdot 2^{2}+2 \cdot 3\right): 13\right]^{3} \)

To solve the expression step by step, let's break it down: 1. Simplify inside the parentheses: \[ 2 \cdot 5 - 14 : 2 = 10 - 7 = 3 \] 2. Substitute that back into the expression: \[ 74 \left[ 10 \cdot 3 - 3^{2} \right] : 3 + \left[ \left( 5 \cdot 2^{2} + 2 \cdot 3 \right) : 13 \right]^{3} \] Calculate \(3^2 = 9\): \[ 10 \cdot 3 - 9 = 30 - 9 = 21 \] 3. Now the expression looks like: \[ 74 \cdot 21 : 3 + \left[ \left( 5 \cdot 4 + 6 \right) : 13 \right]^{3} \] 4. Calculate \(74 \cdot 21\): \[ 74 \cdot 21 = 1554 \] Now we can divide: \[ 1554 : 3 = 518 \] 5. Now simplifying the right side: \[ 5 \cdot 4 + 6 = 20 + 6 = 26 \] Now divide by 13: \[ 26 : 13 = 2 \] 6. Finally, calculate \(2^3\): \[ 2^3 = 8 \] 7. Combine everything: \[ 518 + 8 = 526 \] So, the final answer is \(526\).