Đề bài

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

Lời giải chi tiết

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

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