Tính nhanh :
\(\eqalign{ & a)\left( {{2^{78}} + {2^{79}} + {2^{80}}} \right):\left( {{2^{77}} + {2^{76}} + {2^{75}}} \right) \cr & b)\left( {{5^{56}} + {5^7}} \right):\left( {{5^{49}} + 1} \right). \cr} \)
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\(\eqalign{ & a)\left( {{2^{78}} + {2^{79}} + {2^{80}}} \right):\left( {{2^{77}} + {2^{76}} + {2^{75}}} \right) \cr & = ({2^{78}} + {2.2^{78}} + {2^2}{.2^{78}}):({2^2}{.2^{75}} + {2.2^{75}} + {2^{75}}) \cr & = {2^{78}}.(1 + 2 + {2^2}):{2^{75}}({2^2} + 2 + 1) \cr & = {2^{78}}:{2^{75}} = {2^{78 – 75}} = {2^3} = 8 \cr & b)\left( {{5^{56}} + {5^7}} \right):\left( {{5^{49}} + 1} \right) \cr & = ({5^7}{.5^{49}} + {5^7}):\left( {{5^{49}} + 1} \right) \cr & = {5^7}\left( {{5^{49}} + 1} \right):\left( {{5^{49}} + 1} \right) \cr & = {5^7} = 78125 \cr} \)