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\(26^{14}>25^{14}=\left(5^2\right)^{14}=5^{28}\)
\(5^{30}=\left(5^3\right)^{10}=125^{10}>124^{10}\)
\(4^{21}=\left(4^3\right)^7=64^7>64^2\)
\(27^{16}.16^9=\left(3^3\right)^{16}.\left(4^2\right)^9=3^{48}.4^{18}>12^{18}=3^{18}.4^{18}\)
\(31^{11}16^{14}=\left(2^4\right)^{14}=2^{56}\)
\(2^{56}>2^{55}\) => \(17^{14}>31^{11}\)
Các bài khác làm tương tự
![](https://rs.olm.vn/images/avt/0.png?1311)
a. \(27^{11}=\left(3^3\right)^{11}=3^{3\cdot11}=3^{33}\)
\(81^8=\left(3^4\right)^8=3^{4\cdot8}=3^{32}\)
Vì 32<33 => 332<333 => 818<2711
b. \(63^{15}=\left(63^5\right)^3=992436543^3\)
\(34^{18}=\left(34^6\right)^3=1544804416^3\)
Vì 992436543<1544804416 nên 9924365433<15448044163 => \(63^{15}< 34^{18}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
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 \(5^{12}< 5^{15}\Rightarrow3^{12}.5^{12}< 3^{12}.5^{15}\Rightarrow15^{12}< 81^3.125^5\)
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![](https://rs.olm.vn/images/avt/0.png?1311)
\(3^{54}\)và \(27^{81}\)
Ta có
\(3^{54}=\left(3^3\right)^{18}=27^{18}\)
Vì \(27^{18}< 27^{81}\Rightarrow3^{54}< 27^{81}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có: 81^11 = ( 9^2 )^11 = 9^22
Vì 9^28 > 9^22
=> 9^28 > 81^11
\(81^{11}=\left(9^2\right)^{^{11}}=9^{2.11}=9^{22}< 9^{28}\)
Vậy \(9^{28}>81^{11}\)