a) 5^270 < 5^300
b) 13^100 < 13^102
c) 3^4995 > 3^4000
So sánh :
a) 125^90 và 25^150
125^90 = (5^3)^90 = 5^270
25^150 = (5^2)^150 = 5^300
125^90 < 25^150
B) 13^100 và 169^51
169^51 = (13^2)^51 = 13^102
13^100 < 169^51
c,243^999 và 9^2000
243^999 = (3^5)^999 = 3^4995
9^2000 = (3^2)^2000 = 3^4000
243^999 > 9^2000
\(\text{a) }125^{90}=\left(5^3\right)^{90}=5^{270}\)
\(25^{150}=\left(5^2\right)^{150}=5^{300}\)
\(\text{Vi }5^{270}< 5^{300}\Rightarrow125^{90}< 25^{150}\)
\(\text{b) }169^{51}=\left(13^{13}\right)^{51}=13^{663}\)
\(\text{Vi }13^{100}< 13^{663}\Rightarrow13^{100}< 13^{663}\)
\(\text{c) }243^{999}>9^{999}>9^{200}\)
\(\Rightarrow243^{999}>9^{200}\)
