Question

[Emily Nain]

1.Tính:

a/ \(\frac{20^{12}\cdot6^{14}}{8^{13}\cdot15^{12}}\)

b/\(\frac{45^{12}\cdot10^{14}}{18^{13}\cdot25^{12}}\)

c/\(\frac{18^{12}\cdot27^8}{6^8\cdot3^{40}}\)

d/\(\frac{12^{14}\cdot9^{18}}{8^9\cdot27^{17}}\)

Answer 1

[Bùi Anh Tuấn]

\(a,\frac{20^{12}\cdot6^{14}}{8^{13}\cdot15^{12}}\)

\(=\frac{5^{12}\cdot2^{24}\cdot2^{14}\cdot3^{14}}{2^{39}\cdot3^{12}\cdot5^{12}}\)

\(=\frac{5^{12}\cdot2^{38}\cdot3^{14}}{2^{39}\cdot3^{12}\cdot5^{12}}=\frac{3^2}{2}=\frac{9}{2}\)

\(b,\frac{45^{12}\cdot10^{14}}{18^{13}\cdot25^{12}}\)

\(=\frac{5^{12}\cdot3^{24}\cdot2^{14}\cdot5^{14}}{2^{13}\cdot3^{26}\cdot5^{24}}\)

\(=\frac{5^{26}\cdot3^{24}\cdot2^{14}}{2^{13}\cdot3^{26}\cdot5^{24}}=\frac{5^2\cdot2}{3^2}=\frac{50}{9}\)

\(c,\frac{18^{12}\cdot27^8}{6^8\cdot3^{40}}\)

\(=\frac{2^{12}\cdot3^{24}\cdot3^{24}}{2^8\cdot3^8\cdot3^{40}}\)

\(=\frac{2^{12}\cdot3^{48}}{2^8\cdot3^{48}}=2^4=16\)

\(d,\frac{12^{14}\cdot9^{18}}{8^9\cdot27^{17}}\)

\(=\frac{3^{14}\cdot2^{28}\cdot3^{36}}{2^{27}\cdot3^{51}}\)

\(=\frac{3^{50}\cdot2^{28}}{2^{27}\cdot3^{51}}=\frac{2}{3}\)

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