100¹¹:105⁸-105³+105⁷=105³-105³+105⁷=105⁷

\(105^5.105^6\div105^8-105^3+105^7\)

\(=105^{11}\div105^8-105^3+105^7\)

\(=105^3-105^3+105^7\)

\(=0+105^7\)

\(=105^7\)

=7^{11 k nha}

= 7⁴⁺⁷=7¹¹

Ta có :\(B=3+3^2+3^3+3^4+....+3^9+3^{10}\)

\(B=\left(3+3^2\right)+\left(3^3+3^4\right)+...+\left(3^9+3^{10}\right)\)

\(B=3.\left(1+3\right)+3^3\left(1+3\right)+....+3^9.\left(1+3\right)\)

\(B=3.4+3^3.4+...+3^9.4\)

\(B=4.\left(3+3^3+....+3^9\right)⋮4\)

\(=>B⋮4\)

Vậy \(B\)có \(⋮\)cho 4

=4x25-3⁴:3²

=100-3²

=100-9

=81

=81 nha bn

k mk nha

mkk lại cho!

= 1 x 2 x 3 + ( - 27 ) - 2 

= 6 + ( - 27 ) - 2

= ( - 21 ) - 2

= - 23

3! + (-9)³ - \(\frac{14}{7}\)

=6 - 729 - 2

= -725

P = 1 +  ( 2² + 2³ ) + ( 2⁴ + 2⁵ ) + ( 2⁶ + 2⁷ )

P = 1 + 2 . ( 1 + 2 ) + 2 . ( 1 + 2 ) + 2 . ( 1 + 2 )

P = 1 + 2 . 3 + 2 . 3 + 2 . 3

Mỗi cặp đều có số 3 

=> P = 1 + 2² + 2³ + 2⁴ + 2⁵ + 2⁶ + 2⁷ chia hết cho 3

\(P=1+2^2+2^3+2^4+2^5+2^6+2^7\)

\(P=1+\left(2^2+2^3\right)+\left(2^4+2^5\right)+\left(2^6+2^7\right)\)

\(P=1+2^2\left(1+3\right)+2^4\left(1+2\right)+2^6\left(1+2\right)\)

\(P=1+2^2.3+2^4.3+2^6.3\)

\(P=\left(1+2^2+2^4+2^6\right).3⋮3\left(đpcm\right)\)

\(3^x+10=13.7\)

\(3^x=91-10\)

\(3^x=81=3^4\)

Vậy x = 4

\(3^x+10=13\times7\)

\(\Rightarrow3^x=91-10\)

\(\Rightarrow3^x=81=3^4\)

\(\Rightarrow x=4\)

2x - 3 = 5⁴ : 5²

2x - 3 = 5^{4 - 2} = 5² = 25

2x = 25 + 3

2x = 28

x = 28 : 2

x = 14

5^{x + 2} = 5³ . 125

5^{x + 2} = 5³ . 5³ = 5^{3 + 3} = 5⁶

=> x = 6 - 2

x = 4

2x-3 =5^4 :5^2

2x - 3 = 5^2 

2x-3 = 25 

2x =22

x = 11

5 ^x+2 = 5^3 x 125

5^x+2  =5^3 x 5^3

5^x+2  = 5^9

x+2 =9

x  = 7