Thực hiện phép tính (tính hợp lí nếu có thể): a) 39 − 125 : [( 5^11 ⋅ 16 + 9 ⋅ 5^11 ) : 5^12]

1) a) \(39 - 125:\left[ {\left( {{5^{11}} \cdot 16 + 9 \cdot {5^{11}}} \right):{5^{12}}} \right]\)

\( = 39 - 125:\left[ {{5^{11}} \cdot \left( {16 + 9} \right):{5^{12}}} \right]\)

\( = 39 - 125:\left[ {{5^{11}} \cdot 25:{5^{12}}} \right]\)

\( = 39 - 125:\left[ {{5^{11}} \cdot {5^2}:{5^{12}}} \right]\)

\[ = 39 - {5^3}:{5^{11 + 2 - 12}}\]

\[ = 39 - {5^3}:{5^1}\]

\[ = 39 - {5^2}\]

\[ = 39 - 25 = 14.\]

b) \[53 \cdot 39 + 47 \cdot 39 - 53 \cdot 21 - 47 \cdot 21\]

\[ = \left( {53 \cdot 39 + 47 \cdot 39} \right) - \left( {53 \cdot 21 + 47 \cdot 21} \right)\]

\[ = 39 \cdot \left( {53 + 47} \right) - 21 \cdot \left( {53 + 47} \right)\]

\[ = 39 \cdot 100 - 21 \cdot 100\]

\[ = 3\,\,900 - 2\,\,100\]

\[ = 1\,\,800\].