Question

Answer 1

\(a.10^{300}=\left(10^3\right)^{100}=1000^{100}\)

Vì \(1000>2=>1000^{100}>2^{100}\)

b. \(2^{161}>2^{160}=\left(2^4\right)^{40}=16^{40}>13^{40}\)

\(=>13^{40}< 2^{161}\)

c. \(3^{2n}=\left(3^2\right)^n=9^n\)

\(2^{3n}=\left(2^3\right)^n=8^n\)

Vì \(9>8=>9^n>8^n=>3^{2n}>2^{3n}\)

d. \(31^{11}< 32^{11}=\left(2^5\right)^{11}=2^{55}< 2^{56}=\left(2^4\right)^{14}=16^{14}< 17^{14}\)

\(=>31^{11}< 17^{14}\)

Answer 2

a: 10^300=(10^3)^100=1000^100>2^100

b: \(3^{2n}=9^n\)

\(2^{3n}=8^n\)

mà 9>8

nên 3^2n>2^3n