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) \(57 \cdot 34 + 100 \cdot 43 + 57 \cdot 66\)

\( = \left( {57 \cdot 34 + 57 \cdot 66} \right) + 100 \cdot 43\)

\( = 57 \cdot \left( {34 + 66} \right) + 100 \cdot 43\)

\( = 57 \cdot 100 + 100 \cdot 43\)

\( = 100 \cdot \left( {57 + 43} \right)\)

\( = 100 \cdot 100\)

\( = 10\,\,000.\)