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a/ 10/7 < 5/8 b/ 49/59 < 63/73 c/12/19 > 11/21
d/ 23/27 < 23231/27271 e/ 13/37 > 21/65 g/ 47/15 > 65/21
mik co the lam sai day ban mho kiem tra lai nhe!
\(26^{14}>25^{14}=\left(5^2\right)^{14}=5^{28}\)
\(5^{30}=\left(5^3\right)^{10}=125^{10}>124^{10}\)
\(4^{21}=\left(4^3\right)^7=64^7>64^2\)
\(27^{16}.16^9=\left(3^3\right)^{16}.\left(4^2\right)^9=3^{48}.4^{18}>12^{18}=3^{18}.4^{18}\)
\(31^{11}16^{14}=\left(2^4\right)^{14}=2^{56}\)
\(2^{56}>2^{55}\) => \(17^{14}>31^{11}\)
Các bài khác làm tương tự
a/
\(37^{1320}=\left(37^2\right)^{660}=1369^{660}\)
\(11^{1979}< 11^{1980}=\left(11^3\right)^{660}=1331^{660}\)
\(\Rightarrow1363^{660}>1331^{660}\Rightarrow37^{1320}>11^{1979}\)
b/
\(27^{11}=\left(3^3\right)^{11}=3^{33}\)
\(81^8=\left(3^4\right)^8=3^{32}\)
\(\Rightarrow27^{11}>81^8\)
d/
\(3^{39}< 3^{40}=\left(3^2\right)^{20}=9^{20}< 9^{21}< 11^{21}\)
e/ \(5^{36}=\left(5^3\right)^{12}=125^{12}\)
\(11^{24}=\left(11^2\right)^{12}=121^{12}\)
\(\Rightarrow5^{36}>11^{24}\)
g/ \(21^{15}=3^{15}.7^{15}\)
\(27.49^8=3^3.\left(7^2\right)^8=3^3.7^{16}\)
\(\frac{21^{15}}{27.49^8}=\frac{3^{15}.7^{15}}{3^3.7^{16}}=\frac{3^{12}}{7}>1\Rightarrow21^{15}>27.49^8\)
f/ \(199^{20}=\left(199^4\right)^5\)
\(2003^{15}=\left(2003^3\right)^5\)
\(2003^5>1990^5\)
\(\frac{1990^5}{199^4}=\frac{199^5.10^5}{199^4}=199.10^5>1\)
\(\Rightarrow2003^5>1990^5>199^4\Rightarrow2003^{15}>199^{20}\)
a) \(21^{15}=21^{3.5}=\left(21^3\right)^5=9261^5\)
Vì \(9261>27\Rightarrow9261^5>27^5\Rightarrow21^{15}>27^5\)
b) \(15^{12}=\left(3.5\right)^{12}=3^{12}.5^{12}\)
\(81^3.125^5=\left(3^4\right)^3.\left(5^3\right)^5=3^{4.3}.5^{3.5}=3^{12}.5^{15}\)
Vì \(3^{12}=3^{12}\)mà \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)
a) -23/-17 = 23/17
-13/-17 = 13/17
Vì 23>13 => 23/17>13/17
Vậy -23/-17>-13/-17
b) -57/53 = -5301/4929
-97/93 = -5141/4929
Vì -5301<-5141 => -5141/4929< -5301/4929
Vậy -97/93<-57/53
c) 81/-89 = -81/89
-21/29 = -1869/2581
-81/89 = -2349/2581
Vì -1869>-2349 => -2349/2581>-1869/2581
Vậy 81/-89>-21/29