Bài 1: a) (2x+1)^{​2 ​}=​ 25

               (2x+1)^​2 = 5^​2

=> 2x + 1 = 5           hoặc      2x+1 = -5

=> x=2                   hoặc       x=-3

  b) 2^x+2 - 2^​x = 96

<=> 2^​x . 2^​2 - 2^​x = 96

<=> 2^​x(4-1) =96

<=>2^​x = 96 :3 = 32 = 2^​5 

<=> x = 5

c) (x-1)^​3 = 125

<=> (x-1)^​3 = 5^​3

<=> x-1=5

<=>x= 5 +1 = 6

Bài 2 :

a) Ta có :  7^​6+7^​5-7^​4 
              =7^​4(7^​2+7-1) 
              =7^​4.55=7^​4.5.11 chia hết cho 11 

b) Ta có:

81^​7-27^​9-9¹³
=(3^​4)^​7- (3^​3)^​9-^​   (3^​2)^​13 
=3²⁸ - 3²⁷- 3^​26
=3²⁶ (3^​2-3-1) 
 = 3²⁶.5 = 3^1​3.3^​2.5 = 45.3^1​3 chia hết cho 45

Bạn hãy đăng từng bài để tiện trao đổi. Yên tâm mình sẽ giúp bạn.

B1: \(2^{300}=\left(2^3\right)^{100}=8^{100}\) 

\(3^{200}=\left(3^2\right)^{100}=9^{100}\) 

\(8^{100}< 9^{100}\Rightarrow2^{300}< 3^{200}\)

Bài 1:

a) \(\frac{\left(-3\right)^n}{81}=9\Leftrightarrow\left(-3\right)^n=9.81=729\Rightarrow\left(-3\right)^n=\left(-3\right)^6\Rightarrow n=6\)

b) \(\frac{125}{5^n}=5^2\Leftrightarrow\frac{125}{5^n}=25\Rightarrow5^n=125:25=5\Rightarrow n=1\)

Bài 2:

a) \(625^5=\left(5^4\right)^5=5^{4.5}=5^{20}\)

\(125^7=\left(5^3\right)^7=5^{3.7}=5^{21}\)

Thấy: \(5^{20}< 5^{21}\Rightarrow625^5< 125^7\)

b) \(3^{2n}=\left(3^2\right)^n=9^n\) ; \(2^{3n}=\left(2^3\right)^n=8^n\)

\(9^n>8^n\Rightarrow3^{2n}>2^{3n}\)

K cho mình nhé.

A,\(8^2.4^5:2^{20}=\left(2^3\right)^2.\left(2^2\right)^5:2^{20}=2^6.2^{10}:2^{20}=\frac{2^{16}}{2^{20}}=\frac{1}{16}\)

nhan đúng nha

bai 2: a) \(2^{30}=\left(2^3\right)^{10}=8^{10}\)

            \(3^{20}=\left(3^2\right)^{10}=9^{10}\)

vi 8¹⁰ <9¹⁰ nen 2³⁰ <3²⁰

       b)       \(5^{202}=\left(5^2\right)^{101}=25^{101}\)

                 \(2^{505}=\left(2^5\right)^{101}=32^{101}\)

vi 25¹⁰¹ <32¹⁰¹ nen 5²⁰² <2⁵⁰⁵

c) \(333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)

   \(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)

vi 81¹¹¹>64¹¹¹ va 111⁴⁴⁴>111³³³

nen 333⁴⁴⁴>444³³³

bai 3 : \(\left(\frac{1}{3}\right)^{2n-1}=3^5\)

 \(\left(\frac{1}{3}\right)^{2n-1}=\left(\frac{1}{3}\right)^{-5}\)

2n-1=-5

2n=-5+1

2n=-4

n=-4:2

n=-2

Bai 4 : 3x-5/9=0 va 3y+0,4/3=0

           3x=5/9 va 3y=2/15

             x=5/27 va y=2/45

Bai 5:

A=75. {4²⁰⁰².(4²+1)+....+(4²+1)+1)+25

A=75.{4²⁰⁰².20+...+20+1}+25

A=75.{20.(4²⁰⁰²+...+1)+1}+25

A=75.20.(4²⁰⁰²+..+1)+75+25

A=1500.(4²⁰⁰²+...+1)+100

A=100.{15.(4²⁰⁰²+...+1)+1} chia het cho 100

a,=\(\frac{1}{2}\)

b,-80000

 c,\(\frac{1}{16}\)

d,\(1,271734748x10^{29}\)

a) (0.25)^3*32

= (0.5)^5*0.5*2^5

=1^5*0.5

=1*0.5

=0.5

b)(-0.125)^3*80^4

=(-0.125)^3*80^3*80

=(-0.125*80)^3*80

=(-10)^3

=-1000*80

=-80000

c) 8^2*4^5/2^20

=(2³)²*(2²)⁵*2^20

=2^6*2^10*2^20

=2^36

d)81^11*3^17/27^10*9^15

=((3⁴)¹¹*3^17)/(3³)¹⁰*(3²)¹⁵

=(3^44*3^17)/(3^30*3^30)

=3^61/3^60

=3

Bài b) dòng thứ 3 từ dưới đếm lên, phải là, (-10)^3*80 nha, gấp quá mình ghi nhầm ;)