1) \(5^{199}< 5^{200}=25^{100}\)

\(3^{300}=27^{100}>25^{100}\)

\(\Rightarrow3^{300}>5^{199}\)

\(\Rightarrow\dfrac{1}{3^{300}}< \dfrac{1}{5^{199}}\)

2)  a) \(107^{50}=\left(107^2\right)^{25}=11449^{25}\)

\(73^{75}=\left(73^3\right)^{25}=389017^{25}>11449^{25}\)

\(\Rightarrow107^{50}< 73^{75}\)

b) \(54^4< 5^{12}< 21^{12}\Rightarrow54^4< 21^{12}\)

Giúp mình với

Ta có: \(64^{12}=\left(4^3\right)^{12}=4^{36}\)

\(S=4^0+4^1+...+4^{34}+4^{35}\)

\(\Rightarrow4S=4^1+4^2+...+4^{35}+4^{36}\)

\(\Rightarrow4S-S=4^{36}-4^0\)

\(\Rightarrow3S=4^{36}-1< 4^{36}\)

Vậy \(3S< 64^{12}\)

\(4^0+4^1+4^2+4^3+...+4^{35}\\ 4S=4^1+4^2+4^3+4^4+...+4^{36}\\ 4S-S=\left(4^1+4^2+4^3+4^4+...+4^{36}\right)-\left(4^0+4^1+4^2+4^3+...+4^{35}\right)\\ 3S=4^{36}-1=64^{12}-1\\ Vì64^{12}-1< 64^{12}\\ \Rightarrow3S< 64^{12}\)

\(1>\frac{2}{3}\)

\(1>\frac{3}{4}\)

\(1=\frac{5}{5}\)

\(1< \frac{9}{8}\)

\(1< \frac{12}{2}\)

\(1< \frac{14}{13}\)

\(\frac{2}{3}< 1\)

\(\frac{3}{4}< 1\)

\(\frac{5}{5}=1\)

\(\frac{9}{8}>1\)

\(\frac{12}{2}>1\)

\(\frac{14}{13}>1\)

Ủng hộ tk Đúng nhé bạn ! ^^ 

Câu 1: 3^23  >    5^12

Câu 2: 3^36 < 2^8.11^4

Quy đồng

\(\dfrac{5}{12}< \dfrac{3}{4}\)

143581=3249

Là sao bạn "con lợn hâm" ? Mjk ko hiểu :((