5¹³ : 5¹⁰  - 25 * 2²

= 5^13-10 - 25 * 4

= 5³ - 100

= 125 - 100

= 25

\(S=\dfrac{2^2}{1.2}+\dfrac{2^2}{2.3}+\dfrac{2^2}{3.4}+...+\dfrac{2^2}{2022.2023}\)

\(S=2^2.\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{2022.2023}\right)\)

\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{2022}-\dfrac{1}{2023}\right)\)

\(S=2^2.\left(\dfrac{1}{1}-\dfrac{1}{2023}\right)\)

\(S=2^2.\dfrac{2022}{2023}\)

\(S=\dfrac{2^2.2022}{2023}=\dfrac{8088}{2023}\)

\(B=1+2+2^2+...+2^6.\)

\(=>4B=2^2+2^3+...+2^8\)\(\left(1\right)\)

\(A=2^2+2^3+...+2^8\)\(\left(2\right)\)

Từ (1) và (2) 

=> A = 4B

S = 22 + 42 + 62 + ... + 202

   = (2.1)2 + (2.2)2 + (2.3)2 ... (2.10)2

   = 22.12 + 22.22 + 22.32 + ... + 22.102

   = 22 (12 + 22 + ... + 102 )

   = 4 . 385

   = 1540

= (1x2)^2 (2x2)^2 (3x2)^2 (4x2)^2 ..... (9x2)^2 (10x2)^2 
= 1^2 x 2^2 2^2 x 2^2 3^2 x 2^2 4^2 x 2^2 ..... 9^2 x 2^2 10^2 x 2^2 
= (1^2 2^2 3^2 4^2 ..... 9^2 10^2) x 2^2 
= 385 x 2^2 = 385 x 4 = 1540

a ) ( 13 - 145 + 49 ) - ( 13 + 49 )

= 13 - 145 + 49 - 13 - 49

= ( 13 - 13 ) - 145 + ( 49 - 49 )

= 0 - 145 + 0

= - 145 

b) 25 . 2² . ( 15 - 18 ) + ( 12 - 19 + 10 )

= 25 . 4 . ( -3 ) + 7

= 100 . [ ( -3 ) + 7 ]

= 100 . 4

= 400

a ) ( 13 - 145 + 49 ) - ( 13 + 49 )

= 13 - 145 + 49 - 13 - 49

= ( 13 - 13 ) - 145 + ( 49 - 49 )

= 0 - 145 + 0

= - 145 

( 13 - 145 + 49 ) - ( 13 + 49 )

= 13 - 145 + 49 - 13 - 49

= 13 - 13 + 49 - 49 - 145

= 0 + 0 - 145

= - 145