[(5¹⁶+4¹⁶).3¹⁷.3¹⁰)].(2⁴-4²)

=[(5¹⁶+4¹⁶).3¹⁷.3¹⁰)].(16-16)

=[(5¹⁶+4¹⁶).3¹⁷.3¹⁰)].0

=0

Giải :

[( 5¹⁶ + 4¹⁶ ) . 3¹⁷. 3¹⁰ )] . ( 2⁴- 4² )

= [( 5¹⁶ + 4¹⁶ ) . 3¹⁷. 3¹⁰ )] . [ 24 - ( 2² )²]

= [( 5¹⁶ + 4¹⁶ ) . 3¹⁷. 3¹⁰ )] . [ 24 - 2⁴)

= [( 5¹⁶ + 4¹⁶ ) . 3¹⁷. 3¹⁰ )].0

= 0

\(\dfrac{4^{17}+4^3}{4^{16}+4^2}=\dfrac{4^3\left(4^{14}+1\right)}{4^2\left(4^{14}+1\right)}=\dfrac{4^3}{4^2}=4\)

\(\dfrac{4^{17}+4^3}{4^{16}+4^2}=\dfrac{4^3\left(4^{14}+1\right)}{4^2\left(4^{14}+1\right)}=4\)

3 ×17 + 3 × 25 - 3 × 2 = 3 × (17 + 25 – 2) = 3 × 40 = 120

3x(17+25-2)=3x40=120

10 < 10 + 3

11 + 2=2 + 11

9 < 10 + 9

10 = 10 + 0

17 – 4 > 14 - 3

18 – 4 >12

15 > 15 – 1

17 + 1<17 + 2

12+ 5 > 16

16 =19 - 3

15 – 4 =10 + 1

19 – 3 >11

B=(4+4^2+4^3)+....+(4^15+4^16+4^17)

=4.(4^0+4^1+4^2)+....+4^15.(4^0+4^1+4^2)

=4.(1+4+16)+....+4^15.(1+4+16)

=4.21+...+4^15.21

21.(4+...+4^15) chia hết cho 17

Do B : 17

=> B : 17 dư 0.

sao 21.(4+...+4^15) lại chia hết cho 17

bạn giải thik kĩ đc ko

B=(4+4^2+4^3)+....+(4^15+4^16+4^17)

=4.(4^0+4^1+4^2)+....+4^15.(4^0+4^1+4^2)

=4.(1+4+16)+....+4^15.(1+4+16)

=4.21+...+4^15.21

21.(4+...+4^15) chia hết cho 17

vậy B chia hết cho 17

(\(5^{16}\)+\(16^5\))(\(3^{17}\) -\(3^{10}\))(\(2^4\) -\(4^2\) )

=(\(5^{16}\) +\(16^5\))(\(3^{17}\) -\(3^{10}\))(16-16)

=(\(5^{16}\)+\(16^5\) )(\(3^{17}\) - \(3^{10}\)) .0

=0

Xét \(B=4+4^2+4^3+...+4^{17}\)

      \(B=4+\left(4^2+4^3+4^4+4^5\right)+\left(4^6+4^7+4^8+4^9\right)+...+\left(4^{14}+4^{15}+4^{16}+4^{17}\right)\)

      \(B=4+4^2\left(1+4+4^2+4^3\right)+4^6\left(1+4+4^2+4^3\right)+...+4^{14}\left(1+4+4^2+4^3\right)\)

      \(B=4+4^2\cdot85+4^6\cdot85+...+4^{14}\cdot85\)

      \(B=4+85\left(4^2+4^6+...+4^{14}\right)\)

     \(B=4+17\cdot5\left(4^2+4^6+...+4^{14}\right)\)

      Mà \(17\cdot5\left(4^2+4^6+...+4^{14}\right)⋮17\)

      \(\Rightarrow4+17\cdot5\left(4^2+4^6+...+4^{14}\right)\)chia 17 dư 4

      Hay \(B\)chia 17 dư 4 (ĐPCM)

\(B=4+4^2+4^3+4^4+........+4^{17}\)

\(B=4+\left(4^2+4^4\right)+\left(4^3+4^5\right)+...+\left(4^{15}+4^{17}\right)\)

\(B=4+4^2\left(1+4^2\right)+.....+4^{15}\left(1+4^2\right)\)

\(B=4+4^2.17+....+4^{15}.17\)

\(B=4+17.\left(4^2+4^3+...+4^{15}\right)\)

\(\Rightarrow\)\(17.\left(4^2+4^3+...+4^{15}\right)\)\(⋮17\)

\(\Rightarrow B:17\)\(dư\)\(4\)

\(\text{Vậy B chia 17 dư 4}\)

1: \(=-145\cdot13+145\cdot57+57\cdot10-57\cdot145=-1315\)

2: \(=17\cdot15-17\cdot16+16\cdot17-16\cdot20=255-320=-65\)

3: \(=-38\cdot25+38\cdot4-25\cdot4+25\cdot38=13\cdot4=52\)

4: \(=23\cdot145-23\cdot17-145\cdot23+145\cdot6=479\)

5: \(=24\cdot15-24\cdot4+4\cdot24-4\cdot15=360-60=300\)

6: \(=199\left(15-17+17-5\right)=199\cdot10=1990\)

7: \(=-39\cdot5+39\cdot99+99\cdot10-99\cdot39=795\)

bạn ơi viết rõ cách làm ra