\(S=2+2^3+2^5+....+2^{51}.\)

\(2^2S=2^3+2^5+2^7+....+2^{53}\)

\(4S-S=\left(2^3+2^5+2^7+....+2^{53}\right)-\left(2+2^3+2^5+.....+2^{51}\right)\)

\(3S=2^{53}-2\)

\(S=\frac{2^{53}-2}{3}\)

C = -1 + 3 - 3² + ... + 3²⁰⁰⁹ - 3²⁰¹⁰

=> 3C = - 3 + 3² - 3³ + ... + 3²⁰¹⁰ - 3²⁰¹¹

=> 3C + C = ( - 3 + 3² - 3³ + ... + 3²⁰¹⁰ - 3²⁰¹¹ ) - ( -1 + 3 - 3² + ... + 3²⁰⁰⁹ - 3²⁰¹⁰ )

=> 4C = -3²⁰¹⁰ - 1

=> \(C=\frac{-3^{2010} - 1}{4}\)

\(C=\left(3+3^3+3^5+...+3^{2019}\right)-\left(1+3^2+3^4+...+3^{2020}\right)\)

\(C=\left(1+3+3^2+3^3+...+3^{2020}\right)-2\left(1+3^2+3^4+...+3^{2020}\right)\)

\(A=1+3+3^2+...+3^{2020}\)

\(3A=3+3^2+3^3+...+3^{2021}\)

\(2A=3A-A=3^{2021}-1\Rightarrow A=\frac{3^{2021}-1}{2}\)

\(B=1+3^2+3^4+...+3^{2020}\)

\(3^2B=9B=3^2+3^4+3^6+...+3^{2022}\)

\(8B=9B-B=3^{2022}-1\Rightarrow B=\frac{3^{2022}-1}{8}\)

\(\Rightarrow C=A-2B=\frac{3^{2021}-1}{2}-\frac{2\left(3^{2022}-1\right)}{8}=\frac{2.3^{2021}-3^{2022}+1}{4}\)

\(B=1+4+4^2+...+4^{2020}\)

\(4B=4+4^2+4^3+...+4^{2020}+4^{2021}\)

\(4B-B=\left(4+4^2+4^3+...+4^{2020}+4^{2021}\right)-\left(1+4+4^2+...+4^{2020}\right)\)

\(3B=4^{2021}-1\)

\(B=\frac{4^{2021}-1}{3}\).

TL :

2³ x 3² = 2^{3 + 2} = 2⁵

HT

2³ x 3² = 8 x 9 = 72

Tổng của các số là :

( 199 - 1 ) : 1 + 1 = 199

Đáp số : ..........

199 nha bn

B = ( 4⁵ . 10 . 5⁶ + 25⁵ . 2⁸ ) : ( 2⁸ . 5⁴ + 5⁷ . 2⁵ )

=> B = [ ( 2² )⁵ . 2 . 5 . 5⁶ + ( 5² )⁵ . 2⁸ ] : [ 2⁵ . 5⁴ . ( 2³ + 5³ )]

=> B = ( 2¹⁰ . 2 . 5⁷ +  5¹⁰ . 2⁸ ) : [ 2⁵ . 5⁴ . ( 8 + 125 )]

=> B = [ 2⁸ . 5⁷ . ( 2³ + 5³ )] : ( 2⁵ . 5⁴ . 133 )

=> B = 2⁸ . 5⁷ . 133 : 2⁵ . 5⁴ . 133

=> B = 2³ . 5³ = ( 2 . 5 )³ = 10³ = 1000

= \(\frac{4^5.10.5^6+25^5.2^8}{2^8.5^4+5^7.2^5}\)

= \(\frac{\left(2^2\right)^5.2.5.5^6+\left(5^2\right)^5.2^8}{2^5.5^4\left(2^3+5^3\right)}\)

= \(\frac{2^{11}.5^7+5^{10}.2^8}{2^55^4\left(2^3+5^3\right)}\)

= \(\frac{2^8.5^7\left(2^3+5^3\right)}{2^55^4\left(2^3+5^3\right)}\)

= 2³.5³

= 10³

Tl

= 1000 nha bn

Hok tốt

Ông Kirito vui lòng viết rõ ràng ra đc ko?

\(4.5^5-32:2^4\)

\(=4.3125-32:16\)

\(=12500-2\)

\(=12498\)

=12489 nhabb

b) 2x = 8 x 4

2x = 32

  x = 32 : 2

  x = 16

c) 4x = 16

x = 16 : 4

x = 4

b)2x:4=8                                                                     c)4x=16

2x=8.4                                                                          x=16:4

2x=32                                                                            x=4

x=32:2                                                                           

x=16

a) x².x³:7=224

=>x⁵     :7=224

=>x⁵        =32

=>x⁵ =2⁵ => x=2

b)x³ :x^x +7=8

=>x^3-x       =1

=>x^3-x        =1^3-x

=> x=1

c) xⁿ =1

=> xⁿ=1ⁿ

=> x=1

k cho minh nhee:3