(–2) . (–2) . (–2) . (–3) . (–3) . (–3) = (–2)3 . (–3)3 = [(-2). (-3)]3 = 63

Ta có: A = 1 + 2 + 2² + 2³ + ....... + 2²⁰⁰

=> 2A = 2 + 2² + 2³ + ....... + 2²⁰¹

=> 2A - A = ( 2 + 2² + 2³ + ....... + 2²⁰¹ ) - ( 1 + 2 + 2² + 2³ + ....... + 2²⁰⁰ ) 

=>        A = 2²⁰¹ - 1 

=>  A + 1 = 2²⁰¹

A = 1 + 2 + 2 ^ 2 + 2 ^ 3 + ... + 2 ^ 200

2A = 2 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4 + ... + 2 ^ 201

2A - A = ( 2 + 2 ^ 2 + 2 ^ 3 + 2 ^ 4 + ... + 2 ^ 201 )

           -  ( 1 + 2 + 2 ^ 2 + 2 ^ 3 + ... + 2 ^ 200 )

A         = 2 ^ 201 - 1

=> A + 1 = 2 ^ 201

B = 3 + 3 ^ 2 + 3 ^ 3 + ... + 3 ^ 2005

3B = 3 ^ 2 + 3 ^ 3 + 3 ^ 4 + ... + 3 ^ 2006

3B - B = ( 3 ^ 2 + 3 ^ 3 + 3 ^ 4 + ... + 3 ^ 2006 )

            - ( 3 + 3 ^ 2 + 3 ^ 3 + ... + 3 ^ 2005 )

2B      = 3 ^ 2006 - 3

=> 2B = 3 ^ 2006

Vậy 2B + 3 là lũy thừa của 3

A=1+1+2+2^2+2^3+...+2^200=2=2+2+2^2+2^3+...+2^200=2^2+2^2+2^3+...+2^200

B chia hết cho 3=>2B chia hết cho 3, 3 chia hết cho 3 mà 2B+3 nên 2B+3 chia hết cho 3

a) (-5) . (-5) . (-5) . (-5) . (-5) = (-5)⁵

b) (-2) . (-2) . (-2) . (-3) . (-3) . (-3) = (-2)³.(-3)³

a) ....= (-5)⁵

b) ....= (-2)³.(-3)³

\(6\cdot6\cdot6\cdot6\cdot3\cdot2\)

\(=6\cdot6\cdot6\cdot6\cdot\left(3\cdot2\right)\)

\(=6\cdot6\cdot6\cdot6\cdot6\)

\(=6^5\)

⇒ Chọn D 

D

Chọn D

Chọn C

C 6³ nhé

Câu 3 :

A = 7776 . 8 - 2.243. 64

A = 62208 - 31104

A = 31104

Câu 1 :

a) \(12^5=3^5.4^5\)

b) \(20^6=4^6.5^6\)

c) \(54^3=6^3.9^3\)

Câu 2 :

a) \(3.5^{55}=3.\left(5^5\right)^{11}\)

b) \(4.3^{816}=4.\left(3^{17}\right)^{48}\)

c) \(9.8.7^{6412}=9.8.\left(7^{28}\right)^{229}\)

a.=\(\left(-5\right)^5\)

b. =\(\left(-2\right)^3\cdot\left(-3\right)^3\)

=\(6^3\)

a {-5}⁵

^{b {-2}3 . {-3}3 ={-2 .-3 }3={-6]3}

\(\begin{array}{l}{3^3}{.3^4} = {3^{3 + 4}} = {3^7};\\{10^4}{.10^3}  = 10^{4+3}= {10^7};\\{x^2}.{x^5} = x^{2+5} = {x^7}.\end{array}\

a) \(\left(-5\right)\left(-5\right)\left(-5\right)\left(-5\right)\left(-5\right)=\left(-5\right)^5\)

b)\(\left(-2\right)\left(-2\right)\left(-2\right)\left(-3\right)\left(-3\right)\left(+3\right)=\left(-2\right)^3\cdot\left(-3\right)^2\cdot3=\left(-2\right)^3\cdot3^3\)

c) \(\left(-7\right)\cdot7\cdot5\cdot\left(-5\right)\left(-5\right)=\left(-7^2\right)\cdot\left(-5\right)^3\)

d) \(\left(-8\right)\left(-3\right)3\cdot125=\left(-2^3\right)\cdot\left(-3^2\right)\cdot5^3\)

e) \(27\cdot\left(-2\right)3\left(-7\right)\cdot49=3^4\cdot\left(-2\right)\cdot\left(-7^3\right)\)