giúp ẻm câu 11 đến 22 với
11.
\(9^5=\left(3^2\right)^5=3^{10}\)
\(27^3=\left(3^3\right)^3=3^9\)
Do \(10>9\Rightarrow3^{10}>3^9\)
\(\Rightarrow9^5>27^3\)
12.
\(3^{500}=\left(3^5\right)^{100}=243^{100}\)
\(7^{300}=\left(7^3\right)^{100}=343^{100}\)
Do \(343>243\) nên \(343^{100}>243^{100}\)
Vậy \(7^{300}>3^{500}\)
13.
\(8^5=\left(2^3\right)^5=2^{15}\)
\(3.4^7=3.\left(2^2\right)^7=3.2^{14}>2.2^{14}=2^{15}\)
Vậy \(3.4^7>8^{15}\)
14.
\(202^{303}=\left(202^3\right)^{101}=\left[\left(2.101\right)^3\right]^{101}=\left(2^3.101^3\right)^{101}=\left(8.101^3\right)^{101}=\left(8.101.101^2\right)^{101}\)
\(=\left(808.101^2\right)^{101}\)
\(303^{202}=\left(303^2\right)^{101}=\left[\left(3.101\right)^2\right]^{101}=\left(3^2.101^2\right)^{101}=\left(9.101^2\right)^{101}\)
Do \(808>9\) nên \(808.101^2>9.101^2\)\
Nên \(\left(808.101^2\right)^{101}>\left(9.101^2\right)^{101}\)
Vậy \(202^{303}>303^{202}\)
15.
\(3^{21}=3.3^{20}=3.\left(3^2\right)^{10}=3.9^{10}\)
\(2^{31}=2.2^{30}=2.\left(2^3\right)^{10}=2.8^{10}\)
Do \(3>2\) và \(9>8\) nên \(3.9^{10}>2.8^{10}\)
Vậy \(3^{21}>2^{31}\)
16.
\(37^{1320}=\left(37^2\right)^{660}=1369^{660}\)
\(11^{1980}=\left(11^3\right)^{660}=1331^{660}\)
Do \(1369>1331\) nên \(1369^{660}>1331^{660}\)
Nên \(37^{1320}>11^{1980}\)
Mà \(11^{1980}>11^{1979}\)
Vậy \(37^{1320}>11^{1979}\)
17.
\(27^5=\left(3^3\right)^5=3^{15}\)
\(243^3=\left(3^5\right)^3=3^{15}\)
Do \(3^{15}=3^{15}\) nên \(27^5=243^3\)
18.
Ta có: \(32^{11}=\left(2^5\right)^{11}=2^{55}\)
\(16^{14}=\left(2^4\right)^{14}=2^{56}\)
Mà \(2^{56}>2^{55}\) nên \(16^{14}>32^{11}\)
Đồng thời: \(17^{14}>16^{14}\) và \(32^{11}>31^{11}\)
Vậy \(17^{14}>31^{11}\)
19.
\(2^{100}=\left(2^2\right)^{50}=4^{50}\)
Do \(4^{50}< 10^{50}\) nên \(2^{100}< 10^{50}\)
20.
\(2^{161}=2.2^{160}=2.\left(2^4\right)^{40}=2.16^{40}\)
Do \(16>13\) nên \(16^{40}>13^{40}\)
Suy ra \(2.16^{40}>13^{40}\)
Vậy \(2^{161}>13^{40}\)
21.
\(333^{444}=\left(333^4\right)^{111}=\left[\left(3.111\right)^4\right]^{111}=\left(3^4.111^4\right)^{111}=\left(81.111.111^3\right)^{111}\)
\(=\left(8991.111^3\right)^{111}\)
\(444^{333}=\left(444^3\right)^{111}=\left[\left(4.111\right)^3\right]^{111}=\left(4^3.111^3\right)^{111}=\left(64.111^3\right)^{111}\)
Do \(8991>64\) nên \(8991.111^3>64.111^3\)
Nên \(\left(8991.111^3\right)^{111}>\left(64.111^3\right)^{111}\)
Vậy \(333^{444}>444^{333}\)
22.
\(3^{200}=\left(3^2\right)^{100}=9^{100}\)
Do \(9>2\) nên \(9^{100}>2^{100}\)
Vậy \(3^{200}>2^{100}\)
11.
Ta có: 95 = (32)5 = 310
Mà: 273 = (33)3 = 39
➩95 > 273
12.
Ta có: 3500 = 35 . 100 = (35)100 = 243100
7300 = 73 . 100 = (73)100 = 343100
Vì 243 < 343 nên 243100 < 343100 hay 3500 < 7300
