1)

75²⁰⁰⁵-75²⁰⁰⁴=75²⁰⁰⁴.75-75²⁰⁰⁴=75²⁰⁰⁴(75-1)=75²⁰⁰⁴.74

75²⁰⁰⁴-75²⁰⁰³=75²⁰⁰³.75-75²⁰⁰³=75²⁰⁰³(75-1)=75²⁰⁰³.74

ta thấy:  75²⁰⁰⁴.74 > 75²⁰⁰³.74

Vậy:  75²⁰⁰⁵-75²⁰⁰⁴ > 75²⁰⁰⁴-75²⁰⁰³

2)

(-32)⁹=  [(-2)⁵  ]⁹ = (-2)^5.9= (-2)⁴⁵ (một số âm vì số mũ lẻ)

Ta thấy: 18¹³ > 16¹³ =[2⁴  ]¹³ = 2⁵² Nên (- 18)¹³< (-2)^{52  (1)}

Mà (2)⁴⁵ < 2⁵²   => (-2)⁴⁵> (-2)^{52     (2)}

Từ (1) và (2) suy ra (-2)⁴⁵ >  (- 18)¹³ hay  (-32)⁹  >  (- 18)¹³ 

\(\text{a) }\left(-\frac{1}{16}\right)^{100}=\frac{\left(-1\right)^{100}}{16^{100}}=\frac{1}{16^{100}}\)

\(\left(-\frac{1}{2}\right)^{500}=\frac{\left(-1\right)^{500}}{2^{500}}=\frac{1}{\left(2^5\right)^{100}}=\frac{1}{32^{100}}\)

Ta co 

\(16^{100}< 32^{100}\)

\(\Rightarrow\frac{1}{16^{100}}>\frac{1}{32^{100}}\)

\(\Rightarrow\left(-\frac{1}{16}\right)^{100}>\left(-\frac{1}{2}\right)^{500}\)

a. 

Ta có:

\(\left(-\frac{1}{16}\right)^{100}=\frac{\left(-1\right)^{100}}{16^{100}}=\frac{1}{16^{100}}\)

\(\left(-\frac{1}{2}\right)^{500}=\frac{\left(-1\right)^{500}}{2^{500}}=\frac{1}{\left(2^5\right)^{100}}=\frac{1}{32^{100}}\)

Vì \(\frac{1}{16^{100}}>\frac{1}{32^{100}}\Rightarrow\left(-\frac{1}{16}\right)^{100}>\left(-\frac{1}{2}\right)^{500}\)

b.

Ta có:

\(\left(-32\right)^9=\left[-\left(2^5\right)\right]^9=-\left(2^{45}\right)\)

\(\left(-16\right)^{13}=\left[-\left(2^4\right)\right]^{13}=-\left(2^{52}\right)\)

Vì \(-\left(2^{45}\right)>-\left(2^{52}\right)\Rightarrow\left(-32\right)^9>\left(-16\right)^{13}\)

#Chúc bạn học tốt!#

d, ta có :(-32)⁹=-(32⁹) ;(-18)¹³=-(18¹³)

32⁹=32\(\times\)32⁸=32\(\times\)(32²)⁴=32\(\times\)1024⁴=32\(\times\)1024\(\times\)1024³

18¹³=18\(\times\)18¹²=18\(\times\)(18³)⁴=18\(\times\)5832⁴=18\(\times\)5832\(\times\)5832³

18\(\times\)5832 >16\(\times\)5832=32\(\times\)2916>32\(\times\)1024 =5832³>1024³ 

nên 18¹³>32⁹

vậy (-18)¹³ <(-32)⁹

(-32)⁹=-(32⁹)

(-18)¹³=-(18¹³)

32⁹<36⁹

ta có :36⁹=(2\(\times\)18)⁹=2⁹\(\times\)18⁹

vì 18⁴>16⁴mà 16⁴=(2⁴)⁴=2¹⁶

mà 2¹⁶>2⁹

^{\(\Rightarrow\)}18⁴>2⁹

^{\(\Rightarrow\)}18⁴\(\times\)18⁹>2⁹\(\times\)18⁹

\(\Rightarrow\)18¹³>36⁹mà 36⁹ >32⁹

\(\Rightarrow\)18¹³>32⁹

\(\Rightarrow\)(-18)¹³<(-32)⁹

32⁹ = (2⁵)⁹ = 2⁴⁵ < 2⁵² = (2⁴)¹³=16¹³<18¹³

=> (-32)⁹ > (-18)¹³

Ta có: \(32^{27}=\left(2^5\right)^{27}=2^{135}\)

\(16^{39}=\left(2^4\right)^{39}=2^{156}\)

mà \(2^{135}< 2^{156}\)

nên \(32^{27}< 16^{39}\)

mà \(16^{39}< 18^{39}\)

nên \(32^{27}< 18^{39}\)

\(\Leftrightarrow-32^{27}>-18^{39}\)

\(\Leftrightarrow\left(-32\right)^{27}>\left(-18\right)^{39}\)

a) ta có: (-32)⁹ = [(-2)⁵ ]⁹ = (-2)⁴⁵ = - (2)⁴⁵ 

(-16)¹³ =  - [ 2⁴ ]¹³ = - (2)⁵²

=> ....

b) ta có: (-5)³⁰ = 5³⁰ = (5³)¹⁰ = 125¹⁰

(-3)⁵⁰ = 3⁵⁰ = (3⁵)¹⁰  = 243¹⁰

=> ....

c) ta có: (-32)⁹ = (-2)⁴⁵ = (-2)¹³ . 2³² 

(-18)¹³ =  [(-2).3² ]¹³ = (-2)¹³ . 3³⁹ 

=> ....

d) ta có: \(\left(-\frac{1}{16}\right)=-\left(\frac{1}{2}\right)^4.\) 

\(\left(-\frac{1}{2}\right)=-\left(\frac{1}{2}\right)^1< -\left(\frac{1}{2}\right)^4\) 

32⁹ = (2⁵)⁹ = 2⁴⁵ = (2³)¹⁵ = 8¹⁵  = 8¹³ . 8² = 8¹³ . 2⁶

18¹³ = 9¹³ . 2¹³ 

Vì 9¹³ > 8¹³

     2¹³ > 2⁶

\(\Rightarrow\)32⁹ < 18¹³

\(\Rightarrow\)\(\left(-32\right)^9>\left(-18\right)^{13}\)

Ta có: 32⁹ = (2⁵)⁹ = 2⁴⁵

18¹³ > 16¹³ = (2⁴)¹³ = 2⁵² (⁴)

Ta thấy : 2⁴⁵ < 2⁵² < 18¹³

=> 32⁹ < 18¹³

Ta có: 32⁹ = (2⁵)⁹ = 2⁴⁵

18¹³ > 16¹³ = (2⁴)¹³ = 2⁵² (⁴)

Ta thấy : 2⁴⁵ < 2⁵² < 18¹³

=> 32⁹ < 18¹³