Question

So sánh các số sau:

d)\(\left(-32\right)^9\)và\(\left(-18\right)^{13}\)

e)\(\left[\frac{-25}{46}\right]\)và\(\left(\frac{-25}{46}\right)^{2005}\)

Answer 1

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

Answer 2

(-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