\(\left(\frac{1}{243}\right)^9=\left(\frac{1}{3^4}\right)^9=\frac{1}{3^{4.9}}=\frac{1}{3^{36}}\)

\(\left(\frac{1}{83}\right)^{13}\frac{1}{3^{42}}\Rightarrow\left(\frac{1}{81}\right)^{13}

Ta thấy:

25^5=(5^2)^5=5^(2*5)=5^10>5^9.

=>1/5^9>1/25^5.

=>-1/5^9<-1/25^5.

=>(-1/5)^9<(-1/25)^5.

Vậy ...

(1/15)^9 < (1/20)^7

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 \(32^{27}< 18^{39}\)

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

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

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