\(27^{11}>81^8;625^5< 125^7;5^{36}>11^{24};5^{28}< 26^{14}\)

\(27^{11}>81^8;625^5< 125^7;5^{36}>11^{24};5^{28}< 26^{14}\)

Hok tốt 

27^11>81^8;625^5<125^7;5^36>11^24;5^28<26^14

17¹⁵ và 2⁵⁹

ta có:

17¹⁵>16¹⁵ ; 16¹⁵= (2⁴)¹⁵=2⁶⁰

Vì 2⁶⁰> 2⁵⁹=>16¹⁵>2⁵⁹

=>17¹⁵>2⁵⁹

\(5^{36}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=\left(11^2\right)^{12}=121^{12}\)

\(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

Ta có: \(5^{36}=\left(5^3\right)^{12}=125^{12}\) 

^{\(11^{24}=\left(11^2\right)^{12}=121^{12}\)} 

Vì 121¹² < 125¹²

Nên 11²⁴ < 5³⁶

\(5^{36}=\left(5^3\right)^{12}=125^{12}\)

\(11^{24}=\left(11^2\right)^{12}=121^{12}\)

Vì \(125^{12}>121^{12}\Rightarrow5^{36}>11^{24}\)

T.I.C.K GIÚP MK NHÉ!

Bài 1:

a, \(64^2=\left(2^6\right)^2=2^{12}\)

\(32^5=\left(2^5\right)^5=2^{25}\)

\(2^{12}< 2^{25}\Rightarrow64^2< 32^5\)

b, \(10^5=\left(5.2\right)^5=5^5.2^5\)

\(5^{10}=5^{5+5}=5^5.5^5\)

\(5^5.2^5< 5^5.5^5\Rightarrow10^5< 5^{10}\)

c, 256^ mấy thế hả bạn?

d, \(9^{200}=\left(9^2\right)^{100}=81^{100}\)

\(81^{100}>10^{100}\Rightarrow9^{200}>10^{100}\)

Bài 2:

\(9.27^2.81^3.216\)

\(=3^2.\left(3^3\right)^2.\left(3^4\right)^3.2^3.3^3\)

\(=3^2.3^6.3^{12}.3^3.2^3\)

\(=3^{2+6+12+3}.2^3\)

\(=3^{23}.2^3\)

Ta có: \(199^{20}=\left(199^4\right)^5=1568239201^5\)

\(2003^{15}=\left(2003^3\right)^5=8036054027^5\)

Vì \(8036054027^5>1568239201^5\) nên \(2003^{15}>199^{20}\)

Ta có :

199²⁰ < 216²⁰ = ( 6³ )²⁰ = 6⁶⁰

2003¹⁵ > 1296¹⁵ = ( 6⁴ )¹⁵ = 6⁶⁰

Vì 199²⁰ < 6⁶⁰ < 2003¹⁵

=> 199²⁰ < 2003¹⁵ 

a, Ta có :

\(\left(\frac{1}{2}\right)^{50}=\left(\left(\frac{1}{2}\right)^5\right)^{10}=\left(\frac{1}{32}\right)^{10}\)

bạn so sánh nha :)

b,

T/c : \(99^{20}=\left(\left(99\right)^2\right)^{10}=9801^{10}\)

tiếp đây thì bạn tự làm nha có gì k hiểu ibx mk

Bài 1: \(\frac{2}{3}^6\)

Bài 2: \(2^{24}< 3^{16}\)

ko btttttttttttt

a) 54⁴=3⁴.9⁴.2⁴=3⁴.(3²)⁴.2⁴=3⁴.3⁸.2⁴=3¹².2⁴

21¹²=3¹²7¹² > 3¹².2⁴=54⁴

b)10²⁰=10^2.10=100¹⁰ > 90¹⁰

c)5³⁹=\(\frac{5^{40}}{5}=\frac{5^{2.20}}{5}=\frac{25^{20}}{5}\) < \(\frac{27^{20}}{5}< 27.27^{20}=27^{21}\)