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) \(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)
\(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)
\(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^5+5^7}{1}=5^5+5^7=3125+78125=81250\)
\(\frac{7}{13}.\left(\frac{7}{12}\right)-\frac{5}{12}.\left(\frac{21}{39}\right)+\frac{49}{91}.\left(\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{7}{12}\right)-\frac{5}{12}.\left(\frac{7}{13}\right)+\frac{7}{13}.\left(\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{7}{15}-\frac{5}{12}+\frac{8}{5}\right)=\frac{7}{13}.\left(\frac{33}{20}\right)=\frac{261}{260}\)
A = (5^56 + 5^7) : (5^49 + 1)
A = 5^7.(5^49 + 1) : (5^49 + 1)
A = 5^7.[(5^49 + 1) : (5^49 + 1)]
A = 5^7.1
A = 5^7
(7^22 + 7^21 + 7^20) : (2^5 + 2^4 + 3^2)
= 7^20.(7^2 + 7 + 1) : (2^5 + 2^4 + 3^2)
= 7^20.(49 + 1 + 7) : (32 + 16 + 9)
= 7^20.(50 + 7) : (48 + 9)
= 7^20.57: 57
= 7^20.(57:57)
= 7^20.1
=7^20
\(\frac{5^{56}+5^7}{5^{49}+1}=\frac{5^{49}.5^7+5^7}{5^{49}+1}=\frac{5^7\left(5^{49}+1\right)}{5^{49}+1}=5^7\)