((-)/(5)) 2-7^11 cdot 7^-8 cdot 7^-5=7^4^(11 cdot 8)=7^3=343 d-5^2 cdot 5^-3 9 cdot 2^4: 2^-1 10-2^4: 2^7 1-9: 9^8: 8 4 cdot 9^-1 cdot 6 cdot 3^4 cdot 3^-10 2-(8 cdot 1^5 8^5=4096. 4-(2^1: 2^-1. PanAmerican

Vamos corrigir e resolver cada expressão:<br /><br />1. \( 2 - 7^{11} \cdot 7^{-8} \cdot 7^{-5} = 7^{11 - 8 - 5} = 7^{-2} = \frac{1}{49} \)<br /><br />2. \( d - 5^{2} \cdot 5^{-3} = 5^{2 - 3} = 5^{-1} = \frac{1}{5} \)<br /><br />3. \( 9 \cdot 2^{4} : 2^{-1} = 9 \cdot 2^{4 + 1} = 9 \cdot 2^{5} = 9 \cdot 32 = 288 \)<br /><br />4. \( 10 - 2^{4} : 2^{7} = 10 - 2^{4 - 7} = 10 - 2^{-3} = 10 - \frac{1}{8} = \frac{79}{8} \)<br /><br />5. \( 1 - 9 : 9^{8} : 8 = 1 - \frac{9}{9^{8}} : 8 = 1 - \frac{1}{9^{7}} : 8 = 1 - \frac{1}{8 \cdot 9^{7}} = 1 - \frac{1}{8 \cdot 4782969} = 1 - \frac{1}{38146972656} \approx 1 \)<br /><br />6. \( 4 \cdot 9^{-1} \cdot 6 \cdot 3^{4} \cdot 3^{-10} = 4 \cdot \frac{1}{9} \cdot 6 \cdot 3^{4 - 10} = 4 \cdot \frac{1}{9} \cdot 6 \cdot 3^{-6} = 4 \cdot \frac{1}{9} \cdot 6 \cdot \frac{1}{729} = \frac{24}{6561} \)<br /><br />7. \( 2 - (8 \cdot 1^{5} \cdot 8^{5}) = 2 - 8 \cdot 8^{5} = 2 - 8 \cdot 32768 = 2 - 262144 = -262142 \)<br /><br />8. \( 4 - (2^{1} : 2^{-1}) = 4 - 2^{1 + 1} = 4 - 2^{2} = 4 - 4 = 0 \)<br /><br />Portanto, as respostas corrigidas são:<br /><br />1. \( \frac{1}{49} \)<br />2. \( \frac{1}{5} \)<br />3. \( 288 \)<br />4. \( \frac{79}{8} \)<br />5. \( 1 \)<br />6. \( \frac{24}{6561} \)<br />7. \( -262142 \)<br />8. \( 0 \)