1. \( 2^{3}+\left(3 \cdot 6^{-} 3^{2}\right)-9^{1} \) 2. \( 5 \cdot 6^{-} \cdot 2^{4} \cdot 15^{2}=1^{120}= \) 3) \( 3 \cdot 5-4 \cdot(1+2 \cdot 1)+4 \cdot 6-2^{1}= \)

Let's solve each expression step by step. 1. **Expression:** \( 2^{3}+\left(3 \cdot 6^{-} 3^{2}\right)-9^{1} \) - Calculate \( 2^{3} = 8 \) - Calculate \( 3^{2} = 9 \) - The term \( 6^{-} \) is not standard notation. Assuming it means \( \frac{1}{6} \), we have: \[ 3 \cdot \frac{1}{6} \cdot 9 = \frac{27}{6} = 4.5 \] - Calculate \( 9^{1} = 9 \) - Now substitute back into the expression: \[ 8 + 4.5 - 9 = 8 + 4.5 - 9 = 12.5 - 9 = 3.5 \] **Result:** \( 3.5 \) 2. **Expression:** \( 5 \cdot 6^{-} \cdot 2^{4} \cdot 15^{2}=1^{120} \) - Calculate \( 2^{4} = 16 \) - Calculate \( 15^{2} = 225 \) - Again, assuming \( 6^{-} = \frac{1}{6} \): \[ 5 \cdot \frac{1}{6} \cdot 16 \cdot 225 \] - First, calculate \( 5 \cdot 16 = 80 \) - Then, calculate \( 80 \cdot 225 = 18000 \) - Now, divide by 6: \[ \frac{18000}{6} = 3000 \] - Calculate \( 1^{120} = 1 \) **Result:** \( 3000 = 1 \) (This is not true, so the expression does not hold.) 3. **Expression:** \( 3 \cdot 5-4 \cdot(1+2 \cdot 1)+4 \cdot 6-2^{1} \) - Calculate \( 3 \cdot 5 = 15 \) - Calculate \( 2 \cdot 1 = 2 \), so \( 1 + 2 = 3 \) - Calculate \( 4 \cdot 3 = 12 \) - Calculate \( 4 \cdot 6 = 24 \) - Calculate \( 2^{1} = 2 \) - Now substitute back into the expression: \[ 15 - 12 + 24 - 2 \] - Calculate: \[ 15 - 12 = 3 \] \[ 3 + 24 = 27 \] \[ 27 - 2 = 25 \] **Result:** \( 25 \) ### Summary of Results: 1. \( 3.5 \) 2. \( 3000 = 1 \) (not true) 3. \( 25 \)