Rút gọn
\(A=\frac{3^5\cdot1^7+3^9\cdot5}{3^7\cdot2^5}\)
Những câu hỏi liên quan
\(\frac{1}{10\cdot9}-\frac{1}{9\cdot8}-\frac{1}{8\cdot7}-\frac{1}{7\cdot6}-\frac{1}{6\cdot5}-\frac{1}{5\cdot4}-\frac{1}{4\cdot3}-\frac{1}{3\cdot2}-\frac{1}{2\cdot1}\)
Ta có : \(\frac{1}{10.9}-\frac{1}{9.8}-.....-\frac{1}{2.1}\)
\(=\frac{1}{90}-\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{9.8}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{8}-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\left(1-\frac{1}{9}\right)\)
\(=\frac{1}{90}-\frac{8}{9}=\frac{-79}{90}\)
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Rút gọn:
a,\(A=\frac{5\cdot4^{15}\cdot9^9-4\cdot3^{20}\cdot8^9}{5\cdot2^9\cdot6^{19}-7\cdot2^{29}\cdot27^6}\)
b,\(B=\left(1+\frac{1}{1\cdot3}\right)\left(1+\frac{1}{2\cdot4}\right)\left(1+\frac{1}{3\cdot5}\right)...\left(1+\frac{1}{2014\cdot2016}\right)\)
Rút gọn A=\(\frac{7^{48}\cdot5^{30}\cdot2^8-5^{30}\cdot7^{49}\cdot2^{10}}{5^{29}\cdot2^8\cdot7^{48}}\)
\(A=\frac{7^{48}.5^{30}.2^8-5^{30}.7^{49}.2^{10}}{5^{29}.2^8.7^{48}}=\frac{7^{48}.5^{30}.2^8.\left(1-7.2^2\right)}{5^{29}.2^8.7^{48}}=5.\left(-27\right)=-135\)
Vậy \(A=-135\)
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\(A=\frac{7^{48}.5^{30}.2^8-5^{30}.7^{49}2^{10}}{5^{29}.2^8.7^{48}}\)
\(A=\frac{7^{48}.5^{30}.2^8\left(1-7.2^2\right)}{5^{29}.2^8.7^{48}}\)
\(A=5.\left(-27\right)=-135\)
Vậy \(A=-135\)
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Rút gọn:
a) \(\frac{2^{19}\cdot27+15\cdot4^9\cdot9^4}{6^9\cdot2^{10}+12^{10}}\) c)\(\frac{4^6\cdot9^5+6^9\cdot120}{8^4\cdot3^{12}-6^{11}}\)
b)\(\frac{\left(\frac{2}{5}\right)^7\cdot5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7\cdot5^2+512}\)
\(A=\frac{4}{10\cdot2}+\frac{6}{2\cdot20}+\frac{15}{5\cdot20}+\frac{5}{5\cdot40};B=\frac{3}{1\cdot5}+\frac{5}{13\cdot1}+\frac{11}{13\cdot3}+\frac{2}{3\cdot26}\)
So sánh A với B
Tính nhanh:
\(\frac{\left(\frac{2}{5}\right)^7\cdot5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7\cdot5^2\cdot2^9}\)
Giúp cái nka mấy bn!!!Lm xog giúp mk sẽ chp 5 tik nka!!!Thanks trước...
\(\frac{\left(\frac{2}{5}\right)^7.5^7+\left(\frac{9}{4}\right)^3:\left(\frac{3}{16}\right)^3}{2^7.5^2.2^9}\)
=\(\frac{\left(\frac{2}{5}.5\right)^7+\left(\frac{9}{4}:\frac{3}{16}\right)^3}{2^7.5^2.2^9}\)
=\(\frac{2^7+\left(\frac{9}{4}.\frac{16}{3}\right)^3}{2^7.5^2.2^9}\)
=\(\frac{2^7+3^3.4^3}{2^7.5^2.2^9}\)
=\(\frac{2^7+3^3.2^6}{2^7.5^2.2^9}\)
=\(\frac{2^6.\left(27+2\right)}{2^6.5^2.2^{10}}\)
=\(\frac{29}{25600}\)
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Đoạn \(\frac{2^6\cdot\left(27+2\right)}{2^6\cdot5^2\cdot2^{10}}\)là sai rồi bn ơi!!!
Bn phải lm như mục trên là:
\(\frac{2^6\left(2+3^3\right)}{2^7\left(5^2+2^2\right)}\)\(=\frac{2^6\cdot29}{2^7\cdot29}=\frac{1}{2}\)
Nhưng dù sao cx c.ơn bn vì đã giúp mk,mk sẽ cho bn 1 ths nka!!!
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tính nhanh và ko quy đồng
a] C = \(\frac{5}{2\cdot1}+\frac{4}{1\cdot11}+\frac{3}{11\cdot2}+\frac{1}{2\cdot15}+\frac{13}{15\cdot4}\)
b] B = \(\frac{6}{3\cdot5}+\frac{6}{5\cdot7}+\frac{6}{7\cdot9}+.....+\frac{6}{97\cdot99}\)
a) \(C=\frac{5}{2.1}+\frac{4}{1.11}+\frac{3}{11.2}+\frac{1}{2.15}+\frac{13}{15.4}\)
\(=7\left(\frac{5}{2.7}+\frac{4}{7.11}+\frac{3}{11.14}+\frac{1}{14.15}+\frac{13}{15.28}\right)\)
\(=7\left(\frac{1}{2}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{14}+\frac{1}{14}-\frac{1}{15}+\frac{1}{15}-\frac{1}{28}\right)\)
\(=7\left(\frac{1}{2}-\frac{1}{28}\right)\)
\(=7.\frac{13}{28}=\frac{7.13}{28}=\frac{13}{4}\)
b) \(B=\frac{6}{3.5}+\frac{6}{5.7}+\frac{6}{7.9}+...+\frac{6}{97.99}\)
\(=3\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{97.99}\right)\)
\(=3\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{97}-\frac{1}{99}\right)\)
\(=3\left(\frac{1}{3}-\frac{1}{99}\right)\)
\(=3.\frac{32}{99}=\frac{3.32}{99}=\frac{32}{33}\)
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a, Rút gọn phân số :
\(\frac{\left(-2\right)^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot5^3\cdot2^4\cdot42}\)
b, so sánh không qua quy đồng :
A=\(\frac{-7}{10^{2005}}\)+\(\frac{-15}{10^{2006}}\)
B=\(\frac{-15}{10^{2005}}\)+\(\frac{-7}{10^{2006}}\)
két bn vớ mk . mk bày cho chớ làm vào đây tốn thời gian lắm
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\(A=\frac{\left(-2\right)^3\cdot3^3\cdot5^3\cdot7\cdot8}{3\cdot5^3\cdot2^4\cdot42}\)
\(=\frac{\left(-2\right)^3\cdot3^3\cdot6^3\cdot5^3\cdot7\cdot2^3}{3\cdot5^3\cdot2^4\cdot2\cdot3\cdot7}\)
\(=\frac{\left(-2\right)^3\cdot3^8\cdot5^3\cdot2^3\cdot7}{3^2\cdot5^3\cdot2^5\cdot7}=-2\cdot3^6\)
câu b để nghĩ...
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Rút gọn biểu thức:
\(\frac{2^{12}\cdot13+2^{12}\cdot65}{2^{10}\cdot104}+\frac{3^{10}\cdot11+3^{10}\cdot5}{3^9\cdot2^4}\)
\(\frac{2^{12}.13+2^{12}.65}{2^{10}.104}+\frac{3^{10}.11+3^{10}.5}{3^9.2^4}\)
\(\Rightarrow\frac{2^{12}.\left(13+65\right)}{2^{10}.104}+\frac{3^{10}.\left(11+5\right)}{3^9.2^4}\)
\(\Rightarrow\frac{2^{12}.78}{2^{10}.104}+\frac{3^{10}.2^4}{3^9.2^4}\)
\(=\frac{2^2.3}{4}+3\)
\(=3+3=6\)
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