Rút gọn: 15/30= 3/10.

3/10=3* 3/10* 3= 9/30, 9/10= 9* 3/10* 3= 27/30.

Vì 9/30< 26/30< 27/30 nên 15/50< 26/30< 9/10.

15/50=3/10=9/30

9/10=27/30

=>15/50<26/30<9/10

a)\(10^{20}=\left(10^2\right)^{10}=100^{10}\left(1\right)\)

\(9^{30}=\left(9^3\right)^{10}=729^{10}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow9^{30}>10^{20}\)

b) \(\left(-5\right)^{30}=5^{30}=125^{10}\)

\(\left(-3\right)^{50}=3^{50}=243^{10}\)

\(\Rightarrow\left(-3\right)^{50}>\left(-5\right)^{30}\)

c)\(64^8=\left(2^6\right)^8=2^{48}\)

\(16^{12}=\left(2^4\right)^{12}=2^{48}\)

\(\Rightarrow64^8=16^{12}\)

a: \(\dfrac{-7}{15}=\dfrac{-7\cdot4}{15\cdot4}=\dfrac{-28}{60}\)

\(\dfrac{5}{12}=\dfrac{5\cdot5}{12\cdot5}=\dfrac{25}{60}\)

b: \(\dfrac{1}{5}=\dfrac{1\cdot6}{5\cdot6}=\dfrac{6}{30}\)

\(\dfrac{-2}{3}=\dfrac{-2\cdot10}{3\cdot10}=\dfrac{-20}{30}\)

\(\dfrac{7}{10}=\dfrac{7\cdot3}{10\cdot3}=\dfrac{21}{30}\)

c: \(\dfrac{-15}{50}=\dfrac{-15\cdot3}{50\cdot3}=\dfrac{-45}{150}\)

\(\dfrac{9}{10}=\dfrac{9\cdot15}{10\cdot15}=\dfrac{135}{150}\)

\(\dfrac{26}{-30}=\dfrac{-26}{30}=\dfrac{-26\cdot5}{30\cdot5}=\dfrac{-130}{150}\)

d: \(\dfrac{7}{10}=\dfrac{7\cdot51}{10\cdot51}=\dfrac{357}{510}\)

\(\dfrac{-5}{-15}=\dfrac{1}{3}=\dfrac{1\cdot170}{3\cdot170}=\dfrac{170}{510}\)

\(\dfrac{3}{17}=\dfrac{3\cdot30}{17\cdot30}=\dfrac{90}{510}\)

e: \(\dfrac{-4}{-75}=\dfrac{4}{75}=\dfrac{4}{75}\)

\(\dfrac{-3}{5}=\dfrac{-3\cdot15}{5\cdot15}=\dfrac{-45}{75}\)

\(\dfrac{8}{25}=\dfrac{8\cdot3}{25\cdot3}=\dfrac{24}{75}\)

f: \(-\dfrac{4}{5}=\dfrac{-4\cdot7}{5\cdot7}=\dfrac{-28}{35}\)

\(\dfrac{6}{7}=\dfrac{6\cdot5}{7\cdot5}=\dfrac{30}{35}\)

Ta có:

\(9^{12}=\left(9^6\right)^2=531441^2\)

\(26^2=26^2\)

Vì 531441 > 26 nên 9^12>26^2

9¹² = ( 9⁶ )²

26² = 26²

9⁶ = 531441

Mà 531441 > 26 nên 9¹² > 26² 

9¹²= (9⁶)² = 531441²

Vì 531441> 26=> 531441²> 26²

Vậy 9¹² > 26²

Ta có: \(\dfrac{10^{50}-3}{10^{50}+1}\)<\(\dfrac{10^{50}+1}{10^{50}+1}\)<\(\dfrac{10^{50}+1}{10^{50}-3}\)

=>\(\dfrac{10^{50}-3}{10^{50}+1}\)<​\(\dfrac{10^{50}+1}{10^{50}-3}\)​

vậy (đpcm)

\(\frac{10}{40}=0,25;\frac{9}{50}=0,18;\frac{26}{130}=0,2\)

10³⁰ và 1000²⁰

=>10³⁰=(10³)¹⁰=1000¹⁰

Mà :1000¹⁰<1000²⁰

Vay 10³⁰<1000²⁰

10^30<1000^20

Tick nhé

1000^20=10^60

10^30<10^60

=> 10^30<1000^20

Nho tick nha ban

10³⁰ = (10³)¹⁰ = 1000¹⁰

2¹⁰⁰= (2¹⁰)¹⁰ = 1024¹⁰

Mà 1000¹⁰<1024¹⁰

=> 10³⁰ <2¹⁰⁰

a)10²⁰ và 90¹⁰

Ta có: 10²⁰ =(10²)¹⁰=100¹⁰

Vì 100¹⁰>90¹⁰ nên 10²⁰>90¹⁰

b)(-5)³⁰ và (-3)³⁰

Vì -5<-3 nên (-5)³⁰<(-3)³⁰

b) (-5)³⁰ và (-3)³⁰

Ta có: (-5)³⁰=5³⁰

(-3)³⁰=3³⁰

Vì 5>3 nên (-5)³⁰>(-3)³⁰

a)Ta có : \(10^{20}=\left(10^2\right)^{10}=100^{10}\)

Vì \(100^{10}>90^{10}\Rightarrow10^{20}>90^{10}\)

b)Ta có: \(\left(-5\right)^{30}=\left[\left(-5\right)^2\right]^{15}=25^{15}\)

\(\left(-3\right)^{30}=\left[\left(-3\right)^2\right]^{15}=9^{15}\)

Vì \(25^{15}>9^{15}\Rightarrow\left(-5\right)^{30}>\left(-3\right)^{30}\)

c)Ta có :\(32^9=\left(2^5\right)^9=2^{45}>2^{42}=\left(2^6\right)^7=64^7\\ 6^{13}< 6^{14}=\left(6^2\right)^7=36^7\)

Vì \(2^{45}>64^7>36^7>6^{13}\Rightarrow2^{45}>6^{13}\Rightarrow32^9>6^{13}\)

Vậy \(\left(-32\right)^9>\left(-6\right)^{13}\)