35/37 >13|27

Vì 35×27<37×13

co: 2^91 = (2^13) ^7

5^35 = (5^5)^7

suy ra 2 mu 91 lon hon 5 mu 35

Ta có:

2⁹¹ = (2¹³)⁷ = 8192⁷

5³⁵ = (5⁵)⁷ = 3125⁷

Vì 8192⁷ > 3125⁷

=> 2⁹¹ > 5³⁵

a: \(\left(-\dfrac{1}{16}\right)^{100}=\left(\dfrac{1}{16}\right)^{100}=\left(-\dfrac{1}{2}\right)^{400}\)

\(\left(-\dfrac{1}{2}\right)^{500}=\left(-\dfrac{1}{2}\right)^{500}\)

mà \(400< 500\)

nên \(\left(-\dfrac{1}{16}\right)^{100}< \left(-\dfrac{1}{2}\right)^{500}\)

Ta co : \(\frac{1}{3}+\frac{1}{31}+\frac{1}{35}+\frac{1}{37}+\frac{1}{47}+\frac{1}{53}+\frac{1}{61}

co ai bit chi mjnh cai lun mjnh c.on

Ta có:\(2^{91}=2^{13.7}=\left(2^{13}\right)^7=8192^7\)
\(5^{35}=5^{5.7}=\left(5^5\right)^7=3125^7\)
Vì 8192 > 3125 nên \(2^{91}>5^{25}\)

2⁹¹=(2¹³)⁷=8192⁷

5³⁵=(5⁵)7=3125⁷

Vì 8192>3125 nên 8192⁷>3125⁷ hay 2⁹¹>5³⁵