Tinh nhanh (\(5^{56}+5^7\)):(\(5^{49}+1\))
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\(a;\frac{2^{78}+2^{79}+2^{80}}{2^{77}+2^{76}+2^{75}}=\frac{2^{78}\left(1+2+2^2\right)}{2^{75}\left(1+2+2^2\right)}=2^3=8\)
b) \(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)
\(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)
\(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^5+5^7}{1}=5^5+5^7=3125+78125=81250\)
\(\frac{7}{13}.\left(\frac{7}{12}\right)-\frac{5}{12}.\left(\frac{21}{39}\right)+\frac{49}{91}.\left(\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{7}{12}\right)-\frac{5}{12}.\left(\frac{7}{13}\right)+\frac{7}{13}.\left(\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}+\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{33}{20}\right)=\frac{261}{260}\)
\(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^{49}.5^7+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)