Question

so sanh

a 3^400 va 4^300

b 9^32 va 27^25

c 2^2999 va 3^2001

Answer 1

a, \(3^{400}=\left(3^4\right)^{100}=81^{100}\)

\(4^{300}=\left(4^3\right)^{100}=64^{100}\)

vì \(81^{100}>64^{100}\)

suy ra 3^400 > 4^300

b,  \(9^{32}=\left(3^2\right)^{32}=3^{64}\)

\(27^{25}=\left(3^3\right)^{25}=3^{75}\)

vì  \(3^{64}< 3^{75}\)

suy ra 9^32 < 27^25

c,   có 2 ^2999 < 2^3000 = \(\left(2^3\right)^{1000}=8^{1000}\)

có 3^2001> 3^2000 = \(\left(3^2\right)^{1000}=9^{1000}\)

vì 8^1000 <9^1000

suy ra 2^2999<3^2001

tk mk nhé