Thực hiện phép tính :
\(\frac{2^{10}.3^{31}+2^{90}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)
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thực hiện phép tính :
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}\)
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)
Đặt \(A=\frac{1}{1\cdot3}+\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{99\cdot101}\)
\(2A=\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...+\frac{1}{99}-\frac{1}{101}\)
\(2A=\frac{100}{101}\)
\(A=\frac{50}{101}\)
b) \(\frac{2^{10}+3^{31}+2^{40}+3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}=\frac{2^{10}+2^{40}}{2^{11}+2^{41}}\)
\(\frac{2^{10}+2^{40}}{2^{11}+2^{41}}=\frac{1}{2}\)
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=1/2x(1/1.3+1/3.5+...+1/99.101)
=1/2.(1-1/3+1/3-1/5+1/5-1/7+...+1/99-1/101)
=1/2.(1-1/101)
=1/2.100/101
=50/101
chúc bạn học tốt
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\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)
Tính
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2}{2+2}=\frac{2}{4}=\frac{1}{2}\)
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2^10 .3^6 .3^25 + 2^10 .2^30 .3^6
2 ^11 .3^6 . 3^25 + 2^ 11 . 2^ 30 .3 ^6
2^ 10 . 3^ 6 .(2^ 30 + 3^ 25 )
2^11.3 ^ 6. ( 3^ 25 +2^ 30 )
2 ^ 10. 3^ 6
2^ 11 . 3^6
1
2
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Tính:
f)
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)
Bài làm
\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{11}+2^{41}.3^6}\)
\(=\frac{2^{10}.\left(3^{11}+2^{30}.3^6\right)}{2^{11}.\left(3^{11}+2^{30}.3^6\right)}\)
\(=\frac{1}{2}\)
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# Học tốt #
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\(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}=\frac{2^{10}.3^6\left(3^{25}+2^{30}\right)}{2^{11}.3^6\left(3^{25}+2^{30}\right)}=\frac{1}{2}\)
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\(\frac{2^{10}.2^{31}+2^{40}.3^6}{2^{11}.2^{31}+2^{41}.3^6}\)
\(\frac{2^{10}.2^{31}+2^{40}.3^6}{2^{11}.2^{31}+2^{41}.3^6}\)
\(=\frac{2^{41}+2^{40}.3^6}{2^{42}+2^{41}.3^6}\)
\(=\frac{2^{40}\left(2+3^6\right)}{2^{41}\left(2+3^6\right)}\)
\(=\frac{1}{2}\)
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Thực hiện phép tính:
A=\(\left(3\frac{1}{3}+2,5\right):\left(3\frac{1}{6}-4\frac{1}{5}\right)-\frac{11}{31}\)
B=\(\left(-6\right).10:\left[-0,25+\frac{1}{2}:\left(-2\right)\right]+1\frac{3}{4}\)
A \(=\frac{35}{6}.\left(\frac{-30}{31}\right)-\frac{11}{31}=\frac{-175}{31}-\frac{11}{31}=\frac{-186}{31}=-6\)
\(B=-60:\left(\frac{-1}{2}\right)+\frac{7}{4}=30+\frac{7}{4}=\frac{127}{4}\)
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so sanh A va B
A=2/15 + 2/35 + 2/63 + 2/99 +2/143 va B=11/40
tính M/N
M=4/7*31 + 6/7*41 + 9/10*41 +7/10/57 N=7/19*31 + 5/19*43 + 3/23*43 + 11/23*57
thực hiện phép tính một cách hợp lí
38/11 + ( 16/13 + 6/11 )
Tính:
a/\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)
b/\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)
c/\(\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)
\(\frac{3^{17}\cdot81^{11}}{27^{10}\cdot9^{15}}\)
\(=\frac{3^{17}\cdot\left(3^4\right)^{11}}{\left(3^3\right)^{10}\cdot\left(3^2\right)^{15}}\)
\(=\frac{3^{17}\cdot3^{44}}{3^{30}\cdot3^{30}}\)
\(=\frac{3^{61}}{3^{60}}\)
\(=3\)
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\(\frac{9^2\cdot2^{11}}{16^2\cdot6^3}\)
\(=\frac{\left(3^2\right)^2\cdot2^{11}}{\left(2^4\right)^2\cdot\left(2\cdot3\right)^3}\)
\(=\frac{3^4\cdot2^{11}}{2^8\cdot2^3\cdot3^3}\)
\(=\frac{3^4\cdot2^{11}}{2^{11}\cdot3^3}\)
\(=\frac{3^4}{3^3}\)
\(=3\)
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\(\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2^{11}\cdot3^{31}+2^{41}\cdot3^6}\)
\(=\frac{2^{10}\cdot3^{31}+2^{40}\cdot3^6}{2\cdot\left(2^{10}\cdot3^{31}+2^{40}\cdot3^6\right)}\)
\(=\frac{1}{2}\)
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Xem thêm câu trả lời
Tính giá trị biểu thức sau :
C=(-2)10.331+240.(-3)6/(-2)11.(-3)31+241.36
\(\frac{ }{ }\)
Rút gọn
a) \(\frac{2^{10}.6^{15}+3^{14}.15.4^{13}}{2^{18}.18^7.3^3+3^{15}.2^{25}}\) b) \(\frac{2^{10}.3^{31}+2^{40}.3^6}{2^{11}.3^{31}+2^{41}.3^6}\)