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

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

a)\(\frac{-5}{13}+\left(\frac{3}{5}+\frac{3}{13}-\frac{4}{10}\right)=\frac{-5}{13}-\frac{3}{5}-\frac{3}{13}+\frac{4}{10}=\left(\frac{-5}{13}-\frac{3}{13}\right)+\frac{4}{10}-\frac{3}{5}=\frac{-5-3}{13}+\left(\frac{4}{10}-\frac{6}{10}\right)=\frac{-8}{13}+\frac{-2}{10}=\frac{-80}{130}+\frac{-26}{130}=\frac{-106}{130}=\frac{-53}{65}\)

1)

a) \(\left(-48\right)^3:16^3\)

\(=\left(-48:16\right)^3\)

\(=\left(-3\right)^3\)

\(=-27.\)

b) \(\left(\frac{9}{10}\right)^6:\left(\frac{17}{-20}\right)^6\)

\(=\left(\frac{9}{10}:\frac{17}{-20}\right)^6\)

\(=\left(-\frac{18}{17}\right)^6\)

Chúc em học tốt!

\(\frac{-13^3}{\left(2^3\right)^3}:\frac{\left(-2^5\right)^4}{13^4}\)1.

a, (-48)³:16³

= \(\left(\frac{-48}{16}\right)^3\)

= (-3)³

b,\(\left(\frac{9}{10}\right)^6\):\(\left(\frac{17}{-20}\right)^6\)

= \(\left(\frac{9}{10}:\frac{17}{-20}\right)^6\)

=\(\left(\frac{-18}{17}\right)^6\)

c, \(\left(\frac{-13}{8}\right)^3:\left(\frac{-32}{13}\right)^4\)

= \(\frac{-13^3}{\left(2^3\right)^3}:\frac{\left(-2^5\right)^4}{13^4}\)

= \(\frac{-13^3}{2^9}.\frac{-13^4}{2^{20}}\)

=\(\frac{13^7}{2^{29}}\)

giúp mình đi làm ơn đó.mình cần rất gấp:) :) :)

mk lm rùi nên k cần giúp nx đâu

Bài 2:

=>3^x-1*5=135

=>3^x-1=27

=>x-1=3

=>x=4

Bài 1:

a: \(\left(-\dfrac{1}{16}\right)^{100}=\left(\dfrac{1}{16}\right)^{100}=\left(\dfrac{1}{2}\right)^{400}< \left(\dfrac{1}{2}\right)^{500}=\left(-\dfrac{1}{2}\right)^{500}\)

b: \(\left(-32\right)^9=\left(-2^5\right)^9=-2^{45}=-2^{13}\cdot2^{32}\)

\(\left(-18\right)^{13}=\left(-2\cdot3^2\right)^{13}=-2^{13}\cdot3^{26}\)

mà 2^32<3^26

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

c: \(\left(0.37\right)^{100}>0>\left(-2\right)^{101}\)

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

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

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

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

Vế trái: 4/(x+2).(x+6)+7/(x+6).(x+13)

<=>1/x+2 -1/x+6 +1/x+6 -1/x+13

<=>1/x+2-1/x+13

=> 1/x+2-1/x+13=2x+1/(x+2).(x+16) -3/(x+13).(x+16)

<=>1/x+2 - 1/x+13 + 1/x+13 - 1/x+16=2x+1/(x+2).(x+16)

<=>1/x+2 - 1/x+16=2x+1/(x+2).(x+16)

<=> 14/(x+2).(x+16)= 2x+1/(x+2).(x+16)

<=> 2x+1=14

<=> 2x=14-1

<=> 2x=13

<=> x=13:2

<=> x=13/2

Vậy x=13/2

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