2¹⁶¹ > 2¹⁶⁰ = 2^4.40 = (2⁴)⁴⁰ = 16⁴⁰ > 13⁴⁰

a, 7 . 2 ¹³ va 2¹⁶

14¹³    ;   2¹⁶ . Nhu vay  14¹³ > 2¹⁶

b, 21¹⁵ va 27⁵ . 49⁸

21¹⁵  ;  1323¹³ . Nhu vay 21¹⁵ < 1323¹³

c, 72⁴⁵ - 72⁴⁴ va 72⁴⁴ - 72⁴³

72 ; 72 . Nhu vay 72 = 72

d,10³⁰ va 2¹⁰⁰

10³⁰ > 2¹⁰⁰ vi 10+10+10+..+10[ 30 lan nhu vay]

e,333⁴⁴⁴ va 444³³³

333⁴⁴⁴ = 444³³³

j, 13⁴⁰ va 2¹⁶¹

13⁴⁰ < 2¹⁶¹ vi 40 < 161 

g,5³⁰⁰ va 3⁴⁵³

5³⁰⁰ < 3⁴⁵³ vi 300<453

13⁴⁰ và 2¹⁶¹

Ta có :

2¹⁶¹ > 2¹⁶⁰ = ( 2⁴)⁴⁰ = 16⁴⁰

Vì 16 > 13

Nên 13⁴⁰ < 2¹⁶¹

số số hạng của dãy trên là:(40-11):1+1=30

Vì:\(\frac{1}{11}=\frac{1}{11},..........,\frac{1}{40}< \frac{1}{11}\)

\(\Rightarrow\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+\frac{1}{14}< \frac{1}{11}.30=\frac{30}{11}< 1\)

\(\Rightarrow\frac{1}{11}+.....+\frac{1}{40}< 1\)

Vậy,A<1.

TICK HỘ TUI CÁI!!!!!!

thanks

Bài 1:

Ta có:

\(\left(\frac{1}{10}\right)^{15}=\left(\frac{1}{5}\right)^{3.5}=\left(\frac{1}{125}\right)^5\)

\(\left(\frac{3}{10}\right)^{20}=\left(\frac{3}{10}\right)^{4.5}=\left(\frac{81}{10000}\right)^5\)

Lại có:

\(\frac{1}{125}=\frac{80}{10000}< \frac{81}{10000}\Rightarrow\left(\frac{1}{125}\right)^5< \left(\frac{81}{10000}\right)^5\)

\(\Rightarrow\left(\frac{1}{10}\right)^{15}< \left(\frac{3}{10}\right)^{20}\)

Bài 2:

Ta có:

\(A=\frac{13^{15}+1}{13^{16}+1}\Rightarrow13A=\frac{13^{16}+13}{13^{16}+1}=1+\frac{12}{13^{16}+1}\)

\(B=\frac{13^{16}+1}{13^{17}+1}\Rightarrow13B=\frac{13^{17}+13}{13^{17}+1}=1+\frac{12}{13^{17}+1}\)

Mà \(\frac{12}{13^{16}+1}>\frac{12}{13^{17}+1}\)

\(\Rightarrow1+\frac{12}{13^{16}+1}>1+\frac{12}{13^{17}+1}\)

\(\Rightarrow13A>13B\Rightarrow A>B\)

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   \(\frac{13}{53}< \frac{11}{30}\).

a) 13/57=13+16/57+16=29/73   ( Ghi nhớ SKG Toán 6)
-=> 13/57 < 29/73
b)  17/42 = 17-4/42-4 = 13/38
=> 17/42 > 13/38

c)7/41 = 7+6/41+6= 13/47
=> 7/41<13/47

10^30=(10^3)^10=1000^10

2^100=(2^10)^10=1024^10

=>10^30<2^100

vậy.....

5^40=(5^4)^10=625^10

=>5^40>620^10

\(a,\) Ta có : \(10^{30}=\left(10^3\right)^{10}=1000^{10}\)

                     \(2^{100}=\left(2^{10}\right)^{10}=1024^{10}\)

Vì \(1000^{10}< 1024^{10}\Rightarrow10^{30}< 2^{100}\)

\(b,\)Ta có : \(5^{40}=\left(5^4\right)^{10}=625^{10}\)

Vì \(625^{10}>620^{10}\Rightarrow5^{40}>620^{10}\)