\(\left(3^4\right)^{31}.3\)\(và\)\(\left(4^3\right)^{31}\)

\(81^{31}.3\)và   \(64^{31}\)

\(\Rightarrow3^{125}>4^{93}\)

Có: 3¹²⁵=(3⁴)³¹.3=81³¹.3

       4⁹³=(4³)³¹=64³¹

Vì 81³¹>64³¹

=>81³¹.3>64³¹

=>3¹²⁵>4⁹³

a) Có \(3^{125}=3^{124}.3=\left(3^4\right)^{31}.3=81^{31}.3\)
\(4^{93}=\left(4^3\right)^{31}=64^{31}\)
Vì \(81^{31}>64^{31}\Rightarrow81^{31}.3>64^{31}\)
=) \(3^{125}>4^{93}\)
b) Có \(A=\frac{-7}{10^{2005}}+\frac{-15}{10^{2006}}=\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}\)
\(B=\frac{-15}{10^{2005}}+\frac{-7}{10^{2006}}=\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
Vì \(\frac{-7}{10^{2005}}=\frac{-7}{10^{2005}},\frac{-7}{10^{2006}}=\frac{-7}{10^{2006}},\frac{-8}{10^{2006}}>\frac{-8}{10^{2005}}\)
=) \(\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}>\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
=) A > B 

a) Ta có: 3¹²⁴= (3⁴)³¹= 81³¹

4⁹³= (4³)³¹= 64 ³¹

Do 81³¹ >  64 ³¹ => 3¹²⁴ < 4⁹³ 

Mà 3¹²⁴< 3¹²⁵ => 3¹²⁵ > 4⁹³ 

a ) Ta có :

\(1-\frac{41}{91}=\frac{50}{91}\) \(=\frac{500}{910}\)  ;  \(1-\frac{411}{911}=\frac{500}{911}\)

 Vì \(\frac{500}{910}>\frac{500}{911}\)nên \(\frac{41}{91}< \frac{411}{911}\)

b ) Ta có :

\(1-\frac{113}{115}=\frac{2}{115}\)   ;     \(1-\frac{93}{95}=\frac{2}{95}\)

Vì \(\frac{2}{115}< \frac{2}{95}\)nên \(\frac{113}{115}>\frac{93}{95}\).

c ) Quy đồng TS ta có :

\(\frac{13}{53}=\frac{143}{583}\) ;   \(\frac{11}{30}=\frac{143}{390}\)

Vì \(\frac{143}{583}< \frac{143}{390}\)nên   \(\frac{13}{53}< \frac{11}{30}\).

Đáp án :

93/140 > 63/97 > 31/49

ko có cách giải , tự tìm hiểu

ủng hộ tớ nha

93/140 > 63/97 > 31/49

ai tk mình mình tk lại cho

\(~~~HD~~~\)

\(\frac{90}{93}=1-\frac{3}{93};\frac{190}{193}=1-\frac{3}{193}\)

Vì: 93<193 nên: \(\frac{3}{93}>\frac{3}{193}\Rightarrow\frac{90}{93}< \frac{190}{193}\)

Vậy: \(\frac{90}{93}< \frac{190}{193}\)

ta có :

\(\frac{90}{93}< \frac{190}{193}\)

Ta có:

+)\(125^{80}=\left(5^3\right)^{80}=5^{240}\)

+)\(25^{118}=\left(5^2\right)^{118}=5^{236}\)

Vậy 5^240>5^236

=> 125^80>25^118

125^80 và 25^118

( 5^3 )^80 và ( 5^2 )^118]

5^240 và 5^236

Vì 240 > 236 nên 5^240 > 5^236 hay 125^80 > 25^118

4^5<64²

36²>6⁵

125⁴>25³

GIẢi THÍCH RÕ RA HỘ MK

Ta có :

\(625^5=\left(5^4\right)^5=5^{20}\)

\(125^7=\left(5^3\right)^7=5^{21}\)

Vì 20 < 21 nên \(5^{20}< 5^{21}\)hay \(625^5< 125^7\)

~ Hok tốt ~