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a, => 2^x = (2^3)^4/(2^4)^3 = 2^12/2^12 = 1 = 2^0
=> x = 0
c, => 4^x = 4^10.(4-3) = 4^10
=> x=10
d, => 2^2.3^x-1 + 2.3^x.9 = 2^2.3^6+2.3^9
=> 2.3^x-1 . (2+3.9) = 2.3^6.(2+3^3)
=> 2.3^x-1 . 27 = 2.3^6 . 27
=> 3^x-1 = 3^6
=> x-1 = 6
=> x = 7
e, => 2^x.(1/3+1/6+2) = 2^11.(2+1/2)
=> 2^x. 5/2 = 2^11. 5/2
=> 2^x = 2^11
=> x = 11
Tk mk nha
\(A=2^7+2^8+2^9+2^{10}+...+2^{34}\)
\(\Rightarrow2A=2\left(2^7+2^8+2^9+2^{10}+...+2^{34}\right)\)
\(\Rightarrow2A=2^8+2^9+2^{10}+...+2^{35}\)
\(\Rightarrow2A-A=\left(2^8+2^9+2^{10}+...+2^{35}\right)-\left(2^7+2^8+2^9+2^{10}+...+2^{34}\right)\)
\(\Rightarrow A=2^{35}-2^7\)
\(A=2^7+2^8+2^9+2^{10}+...+2^{34}\\ 2A=2^8+2^9+2^{10}+2^{11}+...+2^{35}\\ 2A-A=\left(2^8+2^9+2^{10}+2^{11}+...+2^{35}\right)-\left(2^7+2^8+2^9+2^{10}+...+2^{34}\right)\\ A=2^{35}-2^7\)
1.Ta có A= 710 +79 - 78
A= 78 .(72 +7 -1)
A=78 .55
=> A chia hết cho 11( vì có thừa số 55 chia hết cho 11)
Lời giải:
Ta có:
\(A=\left(5+\frac{1}{5}-\frac{2}{9}\right)-\left(2-\frac{1}{23}-2\frac{3}{35}+\frac{5}{6}\right)-\left(8+\frac{2}{7}-\frac{1}{18}\right)\)
\(A=5+\frac{1}{5}-\frac{2}{9}-2+\frac{1}{23}+2+\frac{3}{35}-\frac{5}{6}-8-\frac{2}{7}+\frac{1}{18}\)
\(A=\left(5-2+2-8\right)+\left(\frac{1}{5}+\frac{3}{35}-\frac{2}{7}\right)-\left(\frac{2}{9}+\frac{5}{6}-\frac{1}{18}\right)+\frac{1}{23}\)
\(A=-3+\left(\frac{7+3-10}{35}\right)-\left(\frac{4+15-1}{18}\right)+\frac{1}{23}\)
\(A=-3+0-1+\frac{1}{23}\)
\(A=-\frac{91}{23}\) . Vậy: \(A=-\frac{91}{23}\)
Chúc bạn học tốt!
Tick cho mình nhé!
a)\(\frac{2^{15}.3^2}{6^6.8^3.4}=\frac{2^{15}.3^2}{2^6.3^6.2^32^2}=\frac{2^{15}.3^2}{2^{\left(6+3+2\right)}.3^6}=\frac{2^{15}.3^2}{2^{11}.3^6}=\frac{2^{\left(15-11\right)}}{3^{\left(6-2\right)}}=\frac{2^3}{3^4}\) viết dài từng bước cho bạn dẽ hiểu
b)\(\frac{8^{10}+4^{10}}{8^4+4^{11}}=\frac{\left(2^3\right)^{10}+\left(2^2\right)^{10}}{\left(2^3\right)^4+\left(2^2\right)^{11}}=\frac{2^{30}+2^{20}}{2^{12}+2^{22}}=\frac{2^{20}\left(2^{10}+1\right)}{2^{12}\left(1+2^{10}\right)}=2^{20-12}=2^8\)có thể đua về cơ số 4 thay cơ 2
129. 62 = (3.4)9. (2.3)2= 39.49. 22.32= 311. (22)9. 22= 311. 220
920. 26 = (32)20. 26 = 340. 26
Bạn tự làm tiếp nhé bởi vì mình không biết đánh phân số
Ta có:\(\frac{12^9.6^2}{9^{20}.2^6}\) \(=\frac{\left(2^2.3\right)^9.\left(2.3\right)^2}{\left(3^2\right)^{20}.2^6}=\frac{2^{18}.3^9.2^2.3^2}{3^{40}.2^6}=\frac{2^{20}.3^{11}}{3^{40}.2^6}\) \(=\frac{2^{14}}{3^{29}}\)
a/ \(\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-\frac{32}{17}+\frac{14}{21}=\left(\frac{15}{34}+\frac{19}{34}\right)+\left(\frac{7}{21}+\frac{14}{21}\right)-\frac{32}{17}=1+1-\frac{32}{17}=\frac{2}{17}\)
a) \(\frac{1}{3}-\left(\frac{1}{2}+\frac{1}{8}\right)\)
= \(\frac{1}{3}-\left(\frac{4}{8}+\frac{1}{8}\right)\)
= \(\frac{1}{3}-\frac{5}{8}\)
= \(\frac{8}{24}-\frac{15}{24}\)
= \(\frac{-7}{24}\)
b) \(\frac{1}{2}-\frac{1}{4}+\frac{1}{13}+\frac{1}{8}\)
= \(\left(\frac{1}{2}-\frac{1}{4}+\frac{1}{8}\right)\)+ \(\frac{1}{13}\)
= \(\left(\frac{4}{8}-\frac{2}{8}+\frac{1}{8}\right)+\frac{1}{13}\)
= \(\frac{1}{8}+\frac{1}{13}\)
= \(\frac{13}{104}+\frac{8}{104}\)
= \(\frac{23}{104}\)
c) \(13\frac{2}{7}:\left(\frac{-8}{9}\right)+2\frac{5}{7}:\left(\frac{-8}{9}\right)\)
= \(\left(13\frac{2}{7}+2\frac{5}{7}\right):\left(\frac{-8}{9}\right)\)
= \(16:\left(\frac{-8}{9}\right)\)
= -18
đặt A = 27 + 28 + 29 + 210 + ... + 234
2A = 28 + 29 + 210 + 211 + ... + 235
2A - A = ( 28 + 29 + 210 + 211 + ... + 235 ) - ( 27 + 28 + 29 + 210 + ... + 234 )
A = 235 - 27
Ta đặt A = 27 + 28 + 29 + 210 + .... + 234
2A= 28 + 29 + 210 + 211 + .... + 235
2A - A = ( 28 + 29 + 210 + 211 + .... + 235 ) - ( 27 + 28 +29 + 210 + ... + 234 )
=> A = 235 - 27