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Ta có: \(M=\left(4^{10}+4^{11}\right)+\left(4^{12}+4^{13}\right)+...+\left(4^{198}+4^{199}\right)\)
\(=4^{10}.\left(1+4\right)+4^{12}.\left(1+4\right)+...+4^{198}.\left(1+4\right)\)
\(=4^{10}.5+4^{12}.5+...+4^{198}.5\)
\(=5.\left(4^{10}+4^{12}+...+4^{198}\right)\text{chia hết cho 5}\)
=> M chia hết cho 5
=> M là B(5) => đpcm.
- Bài 1:
\(A=\frac{2^{10}.13+2^{10}.65}{2^8.104}=\frac{2^{10}.13+2^{10}.13.5}{2^8.2^2.13.2}\)
\(=\frac{2^{10}.13\left(1+5\right)}{2^{10}.13.2}=\frac{2^{10}.13.6}{2^{10}.13.2}=\frac{6}{2}=3\)
\(B=\left(1+2+3+...+100\right)\left(1^2+2^2+3^2+...+100^2\right)\left(65.111-13.15.37\right)\)
\(=\left(1+2+3+...+100\right)\left(1^2+2^2+...+100^2\right)\left(65.111-13.5.3.37\right)\)
\(=\left(1+2+...+100\right)\left(1^2+2^2+...+100^2\right)\left(65.111-65.111\right)\)
\(=\left(1+2+...+100\right)\left(1^2+2^2+...+100^2\right).0\)
\(=0\)
- Bài 2:
\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+100\right)=5750\)
\(x+1+x+2+x+3+...+x+100=5750\)
\(x+x+x+...+x+1+2+3+...+100=5750\)
\(100x+5050=5750\)
\(100x=5750-5050\)
\(100x=700\)
\(x=700:100\)
\(x=7\)
t_i_c_k cho mình nha ^^
\(a,[\left(8.x-12\right):4].3^3.3=3^6.6\)
\(\left(8x-12\right):4=54\)
\(8x-12=216\)
\(8x=228\)
\(x=28,5\)
\(b,41-2^{x+1}=9\)
\(2^{x+1}=41-9\)
\(2^{x+1}=32\)
\(2^{x+1}=2^5\)
\(\Rightarrow x+1=5\)
\(\Rightarrow x=4\)
2) = 19683 . 3 : 59049 + 32 : 16 . 4 - 9 . 1
= 59049 : 59049 + 2 . 4 - 9
= 1 + 8 - 9
= 9 - 9
= 0
1) = {53^3 - 67 . [(169+144)].5 +7.3^4]} :2011
=[53^3 - 67 . (313 . 5 + 7 . 81 ] :2011
= [53^3 - 67. ( 1565 + 567 )] : 2011
= (53^3 - 67 . 2132) :2011
=(148877 - 142844 ) : 2011
= 6033 : 2011
= 3
CÂU 1
\(5^{n+1}+5^n=750\)
\(=>5^n\cdot5+5^n=750\)
\(=>5^n\cdot\left(5+1\right)=750\)
\(=>5^n\cdot6=750\)
\(=>5^n=750:6\)
\(=>5^n=125\)
\(=>5^n=5^3\)
\(=>n=3\)
7x-x=5^21:5^19+3.2^2-7^0
x(7-1)=5^2+3.4-1
x6=25+12-1
x.6=36
x=36:6
x=6
vậy x= 6
7x-x=521:519+3.22-70
=> 6x = 5^2 + 12 -1
=> 6x = 36
=> x = 36/6 = 6
Kết quả 6
Học tốt
a) (105 + 155 - 55) : 55
= 105 : 55 + 155 : 55 - 55 : 55
= 25 + 35 - 1
= 32 + 243 - 1
= 274
a) \(13.57+13.43-190\)
\(=13.\left(57+43\right)-190\)
\(=13.100-190\)
\(=1300-190\)
\(=1110\)
b) \(5^{13}:5^{10}-2^3.2^2-198^0\)
\(=5^3-2^5-1\)
\(=125-32-1\)
\(=93-1\)
\(=92\)