Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
{2^3} - {5^3}:{5^2} + {12.2^2}\\
= 8 - {5^{3 - 2}} + 12.4\\
= 8 - {5^1} + 48\\
= 3 + 48 = 51\\
2,\\
5.\left[ {\left( {85 - 35:7} \right):8 + 90} \right] - 50\\
= 5.\left[ {\left( {85 - 5} \right):8 + 90} \right] - 50\\
= 5.\left[ {80:8 + 90} \right] - 50\\
= 5.\left[ {10 + 90} \right] - 50\\
= 5.100 - 50 = 500 - 50 = 450\\
3,\\
2.\left[ {\left( {7 - {3^3}:{3^2}} \right):{2^2} + 99} \right] - 100\\
= 2.\left[ {\left( {7 - {3^{3 - 2}}} \right):4 + 99} \right] - 100\\
= 2.\left[ {\left( {7 - 3} \right):4 + 99} \right] - 100\\
= 2.\left[ {4:4 + 99} \right] - 100\\
= 2.\left[ {1 + 99} \right] - 100\\
= 2.100 - 100\\
= 200 - 100 = 100\\
4,\\
{2^7}:{2^2} + {5^4}:{5^3}{.2^4} - {3.2^5}\\
= {2^{7 - 2}} + {5^{4 - 3}}{.2^4} - {3.2^5}\\
= {2^5} + {5.2^4} - {3.2^5}\\
= {2^4}.\left( {2 + 5 - 3.2} \right)\\
= {2^4}.1 = 16\\
5,\\
2.\left[ {\left( {95 + {5^2}:5} \right):{2^2} + 180} \right] - {2^2}{.10^2}\\
= 2.\left[ {\left( {95 + 5} \right):4 + 180} \right] - 4.100\\
= 2.\left[ {100:4 + 180} \right] - 400\\
= 2.\left[ {25 + 180} \right] - 400\\
= 2.205 - 400\\
= 410 - 400 = 10\\
6,\\
{3^4}.2 + {2^3}.5 - 7.\left( {{5^7}:{5^5}} \right)\\
= 81.2 + 8.5 - {7.5^{7 - 5}}\\
= 162 + 40 - {7.5^2}\\
= 162 + 40 - 7.25\\
= 202 - 175 = 27\\
7,\\
{5.2^2}{.2^3} - 4.\left( {{5^8}:{5^6}} \right)\\
= {5.2^{2 + 3}} - {4.5^{8 - 6}}\\
= {5.2^5} - {4.5^2}\\
= 5.32 - 4.25\\
= 160 - 100 = 60\\
8,\\
\left( {{3^5}{{.3}^7}} \right):{3^{10}} + {5.2^4} - {7^3}:7\\
= {3^{5 + 7 - 10}} + {5.2^4} - {7^{3 - 1}}\\
= {3^2} + 5.16 - {7^2}\\
= 9 + 80 - 49\\
= 40\\
9,\\
15:\left( {{3^5}:{3^4}} \right) - {2^9}:{2^7}\\
= 15:{3^{5 - 4}} - {2^{9 - 7}}\\
= 15:3 - {2^2}\\
= 5 - 4 = 1\\
10,\\
{5.3^5}:\left( {{3^8}:{3^5}} \right) - {2^3}.5\\
= {5.3^5}:{3^{8 - 5}} - 8.5\\
= {5.3^5}:{3^3} - 40\\
= {5.3^{5 - 3}} - 40\\
= {5.3^2} - 40\\
= 5.9 - 40 = 45 - 40 = 5
\end{array}\)
