a, 2¹.5².17 = 2.25.17 = 50.17 = 850 

b, 2² + 2³ + 2⁴ = 4 + 8 + 16 = 28

c, 2⁵.3 + 2⁴:8 + 50: 5²

= 32.3 + 16:8 + 50:25

=96 + 2 + 2

= 100

d, 11² - 10² - 3²

= 121 - 100 - 9

= 21 - 9

= 12

e, 1³ + 2³ + 3³ + 4³ + 5³

= ( 1+ 2+3+4+5)²

= 15²

= 225

4(x - 5) - 2³ = 2⁴ . 3

4(x - 5) - 8   = 48

4(x - 5)        = 48 + 8 

4(x - 5)         = 56

   x - 5          = 56 : 4

   x - 5          = 14

   x                = 14 + 5

   x                 = 19

Vậy x = 19

4( x - 5 ) - 2^3 = 2^4 . 3

4( x - 5 ) - 8 = 16 . 3

4( x - 5 ) - 8 = 48

4( x - 5 ) = 48 + 8

4( x - 5 ) = 56

x - 5 = 56 : 4

x - 5 = 14

x = 14 + 5

x = 19

Ta có: \(4\left(x-5\right)-2^3=2^4\cdot3\)

\(\Leftrightarrow4\left(x-5\right)=56\)

\(\Leftrightarrow x-5=14\)

hay x=19

`4(x-5)-2^3=2^{4}.3`

`=>4(x-5)-8=16.3=48`

`=>4(x-5)=48+8=56`

`=>x-5=56:4=14`

`=>x=19`

Vậy `x=19`

4.(x-5)-2³=2⁴.3

4.(x-5)-8=16.3

4.(x-5)-8=48

4.(x-5)=48+8

4.(x-5)=56

x-5=56:4

x-5=14

x=14+5

x=19

     4 (x - 5) - 2³ = 2⁴*3

=> 4 (x - 5) - 2³ = 16*3 = 48

=> 4 (x - 5) = 48 + 2³ = 48 + 8 = 56

=> x - 5 = 56/4 = 14

=> x = 14 + 5 = 19

 Vậy x = 19

a) \(5\left(x+7\right)-10=2^3\cdot5\)

\(\Rightarrow5\left(x+7\right)-10=40\)

\(\Rightarrow5\left(x+7\right)=40+10\)

\(\Rightarrow x+7=\dfrac{50}{5}\)

\(\Rightarrow x+7=10\)

\(\Rightarrow x=10-7\)

\(\Rightarrow x=3\)

b) \(9x-2\cdot3^2=3^4\)

\(\Rightarrow9x-18=81\)

\(\Rightarrow9x=81+18\)

\(\Rightarrow9x=99\)

\(\Rightarrow x=\dfrac{99}{9}\)

\(\Rightarrow x=11\)

c) \(5^{25}\cdot5^{x-1}=5^{25}\)

\(\Rightarrow5^{x-1}=5^{25}:5^{25}\)

\(\Rightarrow5^{x-1}=1\)

\(\Rightarrow5^{x-1}=5^0\)

\(\Rightarrow x-1=0\)

\(\Rightarrow x=1\)

a) 5(�+7)−10=23⋅55(x+7)−10=23⋅5

$\Rightarrow 5\left(x+7\right)-10=40$

$\Rightarrow 5\left(x+7\right)=40+10$

⇒�+7=505⇒x+7=550​

$\Rightarrow x+7=10$

$\Rightarrow x=10-7$

$\Rightarrow x=3$

b) 9�−2⋅32=349x−2⋅32=34

$\Rightarrow 9x-18=81$

$\Rightarrow 9x=81+18$

$\Rightarrow 9x=99$

⇒�=999⇒x=999​

$\Rightarrow x=11$

c) 525⋅5�−1=525525⋅5x−1=525

⇒5�−1=525:525⇒5x−1=525:525

⇒5�−1=1⇒5x−1=1

$\Rightarrow$

Mik vẫn chwua hiểu câu hỏi

   2 + 2¹ + 2² + 2³ + ... + 2¹¹

= 2⁰ + 2¹ + 2² + 2³ + ... + 2¹¹

= 2⁰ . ( 1 + 2 + 4 + 8 + 16 + 32 ) + 2⁶ . ( 1 + 2 + 4 + 8 + 16 + 32 )

= 2⁰ . 63 + 2⁶ . 63

= ( 2⁰ + 2⁶ ) . 63 

Do 63 : 9 nên ( 2⁰ + 2⁶ ) . 63 chia hết cho 9 hay 2 + 2¹ + 2² + 2³ + .. + 2¹¹ chia hết cho 9 

Vậy 2 + 2¹ + 2² + 2³ + ... + 2¹¹ chia hết cho 9

A = 2 + 2² + 2³ + 2⁴ + 2⁵ + ... + 2¹⁰⁰

= 2 + 2².(1 + 2 + 2²) + 2⁵.(1 + 2 + 2²) + ... + 2⁹⁸.(1 + 2 + 2²)

= 2 + 7.2² + 7.2⁵ + ... + 7.2⁹⁸)

= 2 + 7.(2² + 2⁵ + ... + 2⁹⁸)

Vậy số dư khi chia A cho 7 là 2

\(A=2+2^2+2^3+2^4+2^5+...+2^{100}\)

\(=\left(2+2^2+2^3\right)+\left(2^4+2^5+2^6\right)+...+\left(2^{97}+2^{98}+2^{99}\right)+2^{100}\)

\(=2\left(1+2+4\right)+2^4\left(1+2+4\right)+...+2^{97}\left(1+2+4\right)+2^{100}\)

\(=7\left(2+2^4+...+2^{97}\right)+2^{100}\)

\(Vì7⋮7=>7\left(2+2^4+..+2^{97}\right)⋮7\)

Ta có:

\(2^3\equiv1\left(mod7\right)\)

\(2^{3.33}\equiv1^{33}\left(mod7\right)\equiv1\left(mod7\right)\)

\(2^{3.33}=2^{99}=>2^{100}=2^{99}.2\equiv1.2\left(mod7\right)\equiv2\left(mod7\right)\)

\(=>2^{100}\) chia \(7\) dư \(2\) mà \(7\left(2+2^4+...+2^{97}\right)⋮7\)

\(=>A\) chia \(7\) dư \(2\)

bn viết cái j mk ko hiểu

Bạn ấy viết như thế này nè :

2 - 2² + 2³ - 2⁴+...+2⁶⁹

\(\text{Đặt A=}2-2^2+2^3-2^4+...+2^{69}\)

\(-2A=2^2+2^3-2^4+2^5-...-2^{70}\)

\(-2A-A\left(-2^2+2^3-2^4+2^5-...-2^{70}\right)-\left(2-2^2+2^3-2^4+..+22^{69}\right)\)

\(-3A=-2-2^{70}\)

\(A=\frac{2+2^{70}}{3}\)

A=