a) \(2^{91}\)và \(5^{35}\)
Ta có :
\(2^{91}=\left(2^{13}\right)^7=8192^7\)
\(5^{35}=\left(5^5\right)^7=3125^7\)
Vì \(8192^7>3125^7\)nên \(2^{91}>5^{35}\)
b) \(3^{4000}\)và \(9^{2000}\)
Ta có :
\(3^{4000}=\left(3^4\right)^{1000}=81^{1000}\)
\(9^{2000}=\left(9^2\right)^{1000}=81^{1000}\)
Vì \(81^{1000}=81^{1000}\)nên \(3^{4000}=9^{2000}\)
\(2^{91}\)và \(5^{35}\)
Ta có :
\(2^{91}=\left(2^{13}\right)^7=8192^7\)
\(5^{35}=\left(5^5\right)^7=3125^7\)
Vì \(8192>3125\)nên \(2^{91}>5^{35}\)
\(3^{4000}\)và \(9^{2000}\)
Ta có :
\(3^{4000}=\left(3^4\right)^{1000}=81^{1000}\)
\(9^{2000}=\left(9^2\right)^{1000}=81^{1000}\)
Vì \(81=81\)nên \(3^{4000}=9^{2000}\)
a/
\(2^{91}=\left(2^7\right)^{13}=128^{13}\)
\(5^{35}< 5^{39}=\left(5^3\right)^{13}=125^{13}\)
\(\Rightarrow2^{91}>5^{35}\)
b/ \(3^{4000}=\left(3^2\right)^{2000}=9^{2000}\)
c/
\(2^{332}< 2^{333}=\left(2^3\right)^{111}=8^{111}\)
\(3^{223}>3^{222}=\left(3^2\right)^{111}=9^{111}\)
\(\Rightarrow3^{223}>2^{332}\)
bài 1 so sánh
a) 2^91 > 5^35
b) 3^4000 = 9^2000
c) 2^332 < 3^223
a) \(2^{91}\)và \(5^{35}\)
\(2^{91}=\left(2^{13}\right)^7\)\(=8192^7\)
\(5^{35}=\left(5^5\right)^7\)\(=3125^7\)
Có \(8192^7>3125^7\)nên \(2^{91}>5^{35}\)
b) \(3^{4000}\)và \(9^{2000}\)
\(3^{4000}=\left(3^2\right)^{2000}\)\(=9^{2000}\)\(=9^{2000}\)
\(\Rightarrow3^{4000}>9^{2000}\)
c) \(2^{332}\)\(< \) \(3^{223}\)
