ta có :

A = 3 + 3² + 3³ + ...+ 3⁵⁹ + 3⁶⁰  

A = ( 3 + 3² + 3³ ) + ( 3⁴ + 3⁵ + 3⁶ ) + ...+ ( 3⁵⁸ + 3⁵⁹ + 3⁶⁰ )

A = 3( 1 + 3 + 3²) + 3⁴(1+3+3²) + ...+ 3⁵⁸(1+3+3² )

A = 3. 13 + 3⁴.13 + ...+ 3⁵⁸.13 

=> A chia hết cho 13 

Ta chú ý : \(3+3^2+3^3=3\left(1+3+9\right)=3.13\)

\(\Rightarrow A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+..+\left(3^{58}+3^{59}+3^{60}\right)\)

\(\Leftrightarrow A=3.13+3^4.13+...+3^{58}.13\)

\(\Leftrightarrow A=13\left(3+3^4+..+3^{58}\right)⋮13\)

Vậy A chia hết cho 13

3mũ2

`3 . 10^2 - [ 2 . 3^2 - (60 - 58)^2 + 25^0]`

`=3.100 - ( 2 .9 - 4 +1)`

`= 3.100 -(18- 4 +1)`

`= 3.100 -(14+1)`

`= 3.100 -15`

`=300-15`

`=285`

\(2+2^2+2^3+2^4+...+2^{59}+2^{60}\\ =\left(2+2^2\right)+\left(2^3+2^4\right)+...+\left(2^{59}+2^{60}\right)\\ =2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\\ =\left(1+2\right)\left(2+2^3+...+2^{59}\right)\\ =3\left(2+2^3+...+2^{59}\right)⋮3\)

a,\(5^3.2-100:4+2^3.5\)

= 125 . 2 - 25 + 8 . 5

= 250 - 25 + 40

= 265

b, \(6^2:9+50.2-3^3.3\)

= 36 : 9 + 100 - 27 . 3

= 4 + 100 - 81

= 23

bạn kia ko làm các ý khác à

b) \(5^3\cdot2-100:4+2^3\cdot5\)

\(=125\cdot2-25+8\cdot5\)

\(=250-25+40\)

\(=225+40=265\)

c) \(6^2:9+50\cdot2+3^3-3\)

\(=36:9+100+27-3\)

\(=4+100+27-3\)

\(=104+27-3=131-3=128\)

d) \(3^2\cdot5+2^3\cdot10-81:3\)

\(=9\cdot5+8\cdot10-27\)

\(=45+80-27\)

\(=125-27=98\)

e) \(5^{13}:5^{10}-25\cdot2^2\)

\(=5^{13-10}-5^2\cdot2^2\)

\(=5^3-\left(5\cdot2\right)^2\)

\(=125-10^2\)

\(=125-100=25\)

f) \(20:2^2+5^9:5^8\)

\(=20:4+5^{9-8}\)

\(=5+5^1=5+5=10\)

g) \(100:5^2+7\cdot3^2\)

\(=10^2:5^2+7\cdot9\)

\(=\left(10:5\right)^2+63\)

\(=2^2+63=4+63=67\)

h) \(84:4+3^9:3^7+5^0\)

\(=21+3^{9-7}+1\)

\(=21+3^2+1\)

\(=21+9+1=30+1=31\)

i) \(29-\left[16+3\cdot\left(51-49\right)\right]\)

\(=29-\left[16+3\cdot2\right]\)

\(=29-\left[16+6\right]\)

\(=29-22=7\)

j) \(\left(15^{19}:5^{17}+3\right)\cdot0:7\)

\(=\left[\left(3\cdot5\right)^{19}:5^{17}+3\right]\cdot0\)

Vì số nào nhân cho 0 cũng bằng 0 nên giá trị biểu thức trên bằng 0

k) \(7^9:7^7-3^2+2^3\cdot5\)

\(=7^{9-7}-9+8\cdot5\)

\(=7^2-9+40\)

\(=49-9+40=40+40=80\)

l) \(1200:2+6^2\cdot2^1+18\)

\(=600+36\cdot2+18\)

\(=600+72+18\)

\(=600+\left(72+18\right)=600+90=690\)

m) \(5^9:5^7+70:14-20\)

\(=5^{9-7}+5-20\)

\(=5^2+5-20\)

\(25+5-20=30-20=10\)

Những câu sau mình làm sau nhé bạn!!!!!!!

:)?

giúp e với em cần gấp ạ

\(A=3^2\cdot4^3-3^2+333\)

\(=3^2\cdot63+333\)

\(=3^2\cdot\left(63+37\right)\)

\(=30^2\)

\(B=5\cdot3^2+4\cdot3^2=3^2\cdot9=9^2\)

ta có

2 mũ 3 = 8

3 mũ 2=9

vì 8<9 nên 2 mũ 3 <3 mũ 2

+) 37 x ( 3 + 7 ) = 3^3 + 3^7

- 37 x ( 3 + 7 ) = 370

- 3^3 + 3^7 = 27 + 2187 = 2214

Từ đó, suy ra => SAI

+) 59 x ( 5 + 9 ) = 5^3 + 9^3

- 59 x ( 5 + 9 ) = 826

- 5^3 + 9^3 = 125 + 729 = 854

Từ đó, suy ra => SAI