Gọi biểu thức trên là S

Ta có : S = 1 + 2 + 2^2 + 2^3 +......... 2^63
=> 2S = 2 x (1 + 2 + 2^2 + 2^3 + ........... + 2^63
=> 2S = 2 + 2^2 + 2^3 +............+ 2^63 + 2^64
------S = 1 + 2 + 2^2 + 2^3 +........+ 2^63
S = 2^64 - 1

đặt A=2²+2²+2³+.....+2¹⁹⁷⁵

=2².2+2³+2⁴+...+2¹⁹⁷⁵

=2³+2³+2⁴+......+2¹⁹⁷⁵

=2³.2+2⁴+2⁵+.........+2¹⁹⁷⁵

=2⁴+2⁴+2⁵+2⁶+.......+2¹⁹⁷⁵

.......

.......

........

=2¹⁹⁷⁴+2¹⁹⁷⁴+2¹⁹⁷⁵

=2¹⁹⁷⁴.2+2¹⁹⁷⁵

=2¹⁹⁷⁵+2¹⁹⁷⁵

=2¹⁹⁷⁵.2

=2¹⁹⁷⁶

vậy.....

Đặt A = 2² + 2² + 2³ + 2⁴ + ..... + 2¹⁹⁷⁵

2A = 2³ + 2³ + 2⁴ + ..... + 2¹⁹⁷⁵ + 2¹⁹⁷⁶

2A - A = (2³ + 2³ + 2⁴ + ..... + 2¹⁹⁷⁵ + 2¹⁹⁷⁶) - (2² + 2² + 2³ + 2⁴ + ..... + 2¹⁹⁷⁵)

A = 2¹⁹⁷⁶ + 2³ - 2² - 2²

A = 2¹⁹⁷⁶ 

so sánh : 5²²⁵ và 2⁵⁷²

Đặt A = 2+2^2+2^3+2^4+....+2^1975

2A=2^2+2^3+2^4+...+2^1976

A=1^1976-2

nke

Đặt A = 2² + 2² + 2³ + ... + 2¹⁹⁷⁵

=> 2A = 2³ + 2³ + 2⁴ + ... + 2¹⁹⁷⁶

=> 2A - A = ( 2³ + 2³ + 2⁴ + ... + 2¹⁹⁷⁶ ) - ( 2² + 2² + 2³ + ... + 2¹⁹⁷⁵ )

=> A = 2³ + 2¹⁹⁷⁶ - 2² - 2² 

Đặt A = 2² + 2² + 2³ + ... + 2¹⁹⁷⁵

=> 2A = 2³ + 2³ + 2⁴ + ... + 2¹⁹⁷⁶

=> 2A - A = ( 2³ + 2³ + 2⁴ + ... + 2¹⁹⁷⁶ ) - ( 2² + 2² + 2³ + ... + 2¹⁹⁷⁵ )

=> A = 2³ + 2¹⁹⁷⁶ - 2² - 2² 

Đặt A = 2² + 2² + 2³ + .... + 2²⁰¹⁷

2A = 2³ + 2³ + .... + 2²⁰¹⁷ + 2²⁰¹⁸

2A - A = (2³ + 2³ + .... + 2²⁰¹⁷ + 2²⁰¹⁸) - (2² + 2² + 2³ + .... + 2²⁰¹⁷)

A = 2³ + 2²¹⁰⁸ - 2² - 2² 

A = 2²⁰¹⁸

1.
a) \(3^4\times3^5\times3^6=3^{4+5+6}=3^{15}\)

b) \(5^2\times5^4\times5^5\times25=5^2\times5^4\times5^5\times5^2=5^{2+4+5+2}=5^{13}\)

c) \(10^8\div10^3=10^{8-3}=10^5\)

d) \(a^7\div a^2=a^{7-2}=a^5\)

2.

\(987=900+80+7\\ =9\times100+8\times10+7\\ =9\times10^2+8\times10^1+7\times10^0\)

\(2021=2000+20+1\\ =2\times1000+2\times10+1\times1\\ =2\times10^3+2\times10^1+1\times10^0\)

\(abcde=a\times10000+b\times1000+c\times100+d\times10+e\times1\\ =a\times10^4+b\times10^3+c\times10^2+d\times10^1+e\times10^0\)

\(A=2^2+2^3+2^4+...+2^{20}\)
\(2A=2^3+2^4+2^5+...+2^{21}\)
\(A=2A-A=2^{21}-2^2\)