Question

So sánh hai số sau:

a) \(3^{200}\)và \(2^{300}\)

b) \(3^{375}\)và \(5^{225}\)

c) \(99^{20}\)và \(9999^{10}\)

d) \(2^{91}\)và \(5^{35}\)

Answer 1

a,\(3^{200}=3^{2.100}=\left(3^2\right)^{100}=9^{100}\)

 \(2^{300}=2^{3.100}=\left(2^3\right)^{100}=8^{100}\)

Vì 9¹⁰⁰>8¹⁰⁰ nên 3²⁰⁰>2³⁰⁰

b,\(3^{375}=3^{5.75}=\left(3^5\right)^{75}=243^{75}\)

\(5^{225}=5^{3.75}=\left(5^3\right)^{75}=125^{75}\)

Vì 243⁷⁵>125⁷⁵ nên 3³⁷⁵>5²²⁵

c,\(99^{20}=99^{2.10}=\left(99^2\right)^{10}=9801^{10}< 9999^{10}\)

Vật 99²⁰<9999¹⁰

d,\(2^{91}=2^{13.7}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=5^{5.7}=\left(5^5\right)^7=3125^7\)

Vì 8192⁷>3125⁷ nên 2⁹¹>5³⁵