2mũ7:2mũ2+5mũ4:5mũ3.2mũ4-3.2mũ5
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đặt A=1+2+2^2+2^3+2^4+2^5+2^6+2^7
2A=2+2^2+2^3+2^4+2^5+2^6+2^7+2^8
2A-A=(2+2^2+2^3+2^4+2^5+2^6+2^7+2^8)-(1+2+2^2+1^3+2^4+2^5+2^6+2^7)
A=2^8-1
A=256-1=255
255 chia hết cho 3
nên 1+2+2^2+2^3+2^4+2^5+2^6+2^7 cũng chia hết cho 3
A = 1 + 2 + 22 + 23 + ...+ 26 + 27
= ( 1 + 2) + ( 22 +23 ) +( 24 + 25 ) + ( 26 + 27) '' có tất cả 8 số chia thành 4 cặp nhé ''
=3 + 22. ( 1 + 2) + 24.(1+2) + 26. ( 1 + 2)
= 3 + 22 .3 + 24.3+ 26 .3
= 3. ( 1 +22 + 24 + 26 ) chia hết cho 3.
\(2016-100.\left(x+11\right)=2^7:2^3\)
\(\Rightarrow\) \(2016-100.\left(x+11\right)=2^4\)
\(\Rightarrow\) \(2016-100.\left(x+11\right)=64\)
\(\Rightarrow\) \(100.\left(x+11\right)=1952\)
\(\Rightarrow\) \(x+11=19,52\)
\(\Rightarrow\) \(x=8,52\)
Study well ! >_<
\(2016-100.\left(x+11\right)=2^7:2^3\)
=> \(2016-100.\left(x+11\right)=2^{7-3}\)
=>\(2016-100.\left(x+11\right)=2^4\)
=> \(2016-100.\left(x+11\right)=16\)
=>\(100.\left(x+11\right)=2016-16=2000\)
=> \(x+11=2000:100=20\)
=> \(x=20-11=9\)
Vậy \(x=9\)
\(A=5+5^2+5^3+5^4+...+5^{39}+5^{40}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{39}+5^{40}\right)\)
\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{39}\left(1+5\right)\)
\(=6\left(5+5^3+...+5^{39}\right)⋮6\)
Suy ra \(A⋮3,A⋮2\).
a,63:62+94=6+94=100
b,135-54:52=135-52=135-25=110
c,73:7-45:43=72-42=49-16=33
d,87:84:82+8=8+8=16.
\(a,6^3:6^2+94=6+94=100\\ b,135-5^4:5^2=135-5^2=135-25=110\\ c,7^3:7-4^5:4^3=7^2-4^2=49-16=33\\ d,8^7:8^4:8^2+8=8^2+8=64+8=72\)
c) 73 : 7 - 45 : 43
= 72 - 42
= 49 - 16
= 33
d) 87 : 84 : 82 + 8
= 8 + 8
= 16
a) 63 : 62 + 94
= 6 + 94
= 100
b) 135 - 54 : 52
= 135 - 52
= 135 - 25
= 110
\(a,6^3:6^2+94=6+94=100\\ b,135-5^4:5^2=135-5^2=110\\ c,7^3:7-4^5:4^3=7^2-4^2=33\\ d,8^7:8^4:8^2+8=8+8=16\)
\(a,6^3:6^2+94=6+94=100\\ b,135-5^4:5^2=135-5^2=135-25=110\\ c,7^3:7-4^5:4^3=7^2-4^2=49-16=33\\ d,8^7:8^4:8^2+8=8+8=16\)
\(\frac{2^7}{2^2}+\frac{5^4}{5^3}.2^4-3.2^5=2^{\left(7-2\right)}+5^{\left(4-3\right)}.2^4-3.2^5=2^5+5^1.2^4-3.2^5\)\(=5.2^4-2.2^5=2^4\left(5-2.2\right)=2^4\)