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\(\frac{27.2^{10}.3^9.32}{6^{12}}\)
\(=\frac{3^3.2^{10}.3^9.2^5}{\left(2.3\right)^{12}}\)
\(=\frac{3^{12}.2^{15}}{2^{12}.3^{12}}=2^3=8\)
E= 29.26:213 = 29+6-13 = 22 = 4
F=35.27.26 = 35.33.26 = 38.26 = 419904
G=64.210 :214 = 26.210 :214 = 26+10-14 = 22 = 4
F=32.128:210 = 25.27:210 = 25+7-10 = 22 = 4
\(\frac{10.\left(4^6.9^5-6^9.120\right)}{8^4.3^{12}-6^{11}}=\frac{10.4^6.9^5-10.6^9.120}{\left(2^3\right)^4.3^{12}-6^{11}}=\frac{2.5.\left(2^2\right)^6.\left(3^2\right)^5-2.5.6^9.2^3.3.5}{2^{12}.3^{12}-6^{11}}\)
\(=\frac{2.5.2^{12}.3^{10}-2^4.3.5^2.6^9}{6^{12}-6^{11}}=\frac{2^{13}.5.3^{10}-6.2^3.5^2.6^9}{6^{11}.\left(6-1\right)}\)
\(=\frac{6^{10}.2^3.5-6^{10}.2^3.5^2}{6^{11}.5}=\frac{6^{10}.2^3.5.\left(1-5\right)}{6^{11}.5}\)
\(=\frac{2^3.\left(-4\right)}{6}=\frac{8.\left(-4\right)}{6}=\frac{-32}{6}=\frac{-16}{3}\)
1 Tính nhanh
a) \(-14+12+\left(-12\right)\left(2^3-7\right)\)
\(=-14+\left[12+\left(-12\right)\right].1\)
\(=-14+0.1\)
\(=-14+0=-14\)
b) \(\left(-5\right)+2\left(-15\right)-\left(-3\right)+\left|-10\right|\)
\(=\left(-5\right)+\left(-30\right)-\left(-3\right)+10\)
\(=\left(-35\right)-\left(-3\right)+10\)
\(=\left(-32\right)+10\)
\(=-22\)
c) \(68.\left(12+32\right)-32.\left(68-12\right)\)
\(=68.44-32.56\)
\(=2992-1792\)
\(=1200\)
d) \(89-\left(-43\right)-32\)
\(=132-32\)
\(=100\)
e) \(-12.\left(-6\right)^2+\left(-4\right)^3.12\)
\(=-12.36+64.12\)
\(=\left(-12+12\right).\left(36+64\right)\)
\(=0+100\)
\(=100\)