(2,0 điểm) Thực hiện phép tính (tính hợp lí nếu có thể):

a) \(4 \cdot {5^2} - 18:{3^2}.\)

b) \[\left( {1\,\,267 - 196} \right) - \left( {267 + 304} \right).\]

c) \[25 \cdot 75 - 3 \cdot 70 + 25 \cdot 125 - 3 \cdot 130.\]

d) \[\left( { - 16} \right) \cdot 125 \cdot \left[ {\left( { - 5} \right) \cdot {2^2}} \right] \cdot {5^4} - 12 \cdot {10^6}.\]

a) \ (4 \ cdot {5^2} - 18: {3^2}.

 

a) \(4 \cdot {5^2} - 18:{3^2}\)

\( = 4 \cdot 25 - 18:9\)

\( = 100 - 2\)

\( = 98\).

c) \[25 \cdot 75 - 3 \cdot 70 + 25 \cdot 125 - 3 \cdot 130\]

\[ = \left( {25 \cdot 75 + 25 \cdot 125} \right) - \left( {3 \cdot 70 + 3 \cdot 130} \right)\]

\[ = 25 \cdot \left( {75 + 125} \right) - 3 \cdot \left( {70 + 130} \right)\]

\[ = 25 \cdot 200 - 3 \cdot 200\]

\[ = 200 \cdot \left( {25 - 3} \right)\]

\[ = 200 \cdot 22\]

\[ = 4\,\,400\].

b) \[\left( {1\,\,267 - 196} \right) - \left( {267 + 304} \right)\]

\[ = 1\,\,267 - 196 - 267 - 304\]

\[ = \left( {1\,\,267 - 267} \right) - \left( {196 + 304} \right)\]

\[ = 1\,\,000 - 500\]

\[ = 500\].

d) \[\left( { - 16} \right) \cdot 125 \cdot \left[ {\left( { - 5} \right) \cdot {2^2}} \right] \cdot {5^4} - 12 \cdot {10^6}\]

\( = \left( { - {2^4}} \right) \cdot {5^3} \cdot \left[ {\left( { - 5} \right) \cdot {2^2}} \right] \cdot {5^4} - 12 \cdot {10^6}\)

\( = \left( { - {2^4} \cdot {2^2}} \right) \cdot \left[ {{5^3} \cdot \left( { - 5} \right) \cdot {5^4}} \right] - 12 \cdot {10^6}\)

\( = \left( { - {2^6}} \right) \cdot \left( { - {5^8}} \right) - 12 \cdot {10^6}\)

\( = {2^6} \cdot {5^8} - 12 \cdot {10^6}\)

\( = {2^6} \cdot {5^6} \cdot {5^2} - 12 \cdot {10^6}\)

\( = {10^6} \cdot 25 - 12 \cdot {10^6}\)

\[ = {10^6} \cdot \left( {25 - 12} \right)\]

\( = {10^6} \cdot 13\)

\( = 13\,\,000\,\,000\).