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24 tháng 12 2023
a: \(A=\dfrac{1-\dfrac{1}{\sqrt{49}}+\dfrac{1}{49}-\dfrac{1}{\left(7\sqrt{7}\right)^2}}{\dfrac{\sqrt{64}}{2}-\dfrac{4}{7}+\left(\dfrac{2}{7}\right)^2-\dfrac{4}{343}}\)
\(=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4-\dfrac{4}{7}+\dfrac{4}{49}-\dfrac{4}{343}}\)
\(=\dfrac{1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}}{4\left(1-\dfrac{1}{7}+\dfrac{1}{49}-\dfrac{1}{343}\right)}=\dfrac{1}{4}\)
b: \(M=1-\dfrac{5}{\sqrt{196}}-\dfrac{5}{\left(2\sqrt{21}\right)^2}-\dfrac{\sqrt{25}}{204}-\dfrac{\left(\sqrt{5}\right)^2}{374}\)
\(=1-\dfrac{5}{14}-\dfrac{5}{84}-\dfrac{5}{204}-\dfrac{5}{374}\)
\(=1-5\left(\dfrac{1}{14}+\dfrac{1}{84}+\dfrac{1}{204}+\dfrac{1}{374}\right)\)
\(=1-5\left(\dfrac{1}{2\cdot7}+\dfrac{1}{7\cdot12}+\dfrac{1}{12\cdot17}+\dfrac{1}{17\cdot22}\right)\)
\(=1-\left(\dfrac{5}{2\cdot7}+\dfrac{5}{7\cdot12}+\dfrac{5}{12\cdot17}+\dfrac{5}{17\cdot22}\right)\)
\(=1-\left(\dfrac{1}{2}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{12}+\dfrac{1}{12}-\dfrac{1}{17}+\dfrac{1}{17}-\dfrac{1}{22}\right)\)
\(=1-\left(\dfrac{1}{2}-\dfrac{1}{22}\right)\)
\(=1-\dfrac{11-1}{22}=1-\dfrac{10}{22}=\dfrac{12}{22}=\dfrac{6}{11}\)
19 tháng 6 2016
a) \(=\left(\left(-\frac{1}{4}-\frac{5}{3}\right)+\frac{7}{33}\right)-\left(-\frac{15}{12}+\frac{6}{11}-\frac{48}{49}\right)\)
\(=\left(-\frac{23}{12}+\frac{7}{33}\right)+\frac{15}{12}-\frac{6}{11}+\frac{48}{49}\)
\(=\left(-\frac{23}{12}+\frac{15}{12}\right)+\left(\frac{9}{33}-\frac{6}{11}\right)+\frac{48}{49}\)
\(=-\frac{2}{3}-\frac{3}{11}+\frac{48}{49}\)
\(=\frac{65}{1617}\)
b) \(=\frac{11}{125}+\left(-\frac{17}{18}+\frac{4}{9}\right)+\left(-\frac{5}{7}+\frac{17}{14}\right)\)
\(=\frac{11}{125}-\frac{1}{2}+\frac{1}{2}\)
\(=\frac{11}{125}\)
V
21 tháng 7 2018
*Trả lời :
a) \(-\dfrac{3}{4}.5\dfrac{3}{13}-0,75.\dfrac{36}{13}\)
= \(-\dfrac{3}{4}.\dfrac{68}{13}-\dfrac{3}{4}.\dfrac{36}{13}\)
=\(\dfrac{3}{4}.\dfrac{-68}{13}-\dfrac{3}{4}.\dfrac{36}{13}\)
=\(\dfrac{3}{4}.\cdot\left(\dfrac{-68}{13}-\dfrac{36}{13}\right)\)
=\(\dfrac{3}{4}.\left(-8\right)\)
= \(-6\)
b)\(4\dfrac{5}{9}:\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)
=\(\dfrac{41}{9}-\left(-\dfrac{5}{7}\right)+\dfrac{49}{9}:\left(-\dfrac{5}{7}\right)\)
=\(\left(\dfrac{41}{9}+\dfrac{49}{9}\right):\left(-\dfrac{5}{7}\right)\)
=\(\dfrac{90}{9}:\left(-\dfrac{5}{7}\right)\)
=\(10:\left(-\dfrac{5}{7}\right)\)
=\(-14\)
c)\(\left(-\dfrac{3}{5}+\dfrac{4}{9}\right):\dfrac{7}{11}+\left(-\dfrac{2}{5}+\dfrac{5}{9}\right):\dfrac{7}{11}\)
=\(\left(-\dfrac{3}{5}\right)+\dfrac{4}{9}:\dfrac{7}{11}+\left(-\dfrac{2}{5}\right)+\dfrac{5}{9}:\dfrac{7}{11}\)(áp dụng tính chất phá ngoặc )
=\(\left\{\left[-\dfrac{3}{5}+\left(-\dfrac{2}{5}\right)\right]+\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\right\}:\dfrac{7}{11}\)
=\(\left(-\dfrac{5}{5}+\dfrac{9}{9}\right):\dfrac{7}{11}\)
=\(\left(-1+1\right):\dfrac{7}{11}\)
\(=0:\dfrac{7}{11}\)
=0.
d)\(\dfrac{6}{7}:\left(\dfrac{3}{26}-\dfrac{3}{13}\right)+\dfrac{6}{7}:\left(\dfrac{1}{10}-\dfrac{8}{5}\right)\)
=\(\dfrac{6}{7}:\left[\dfrac{3}{26}+\left(-\dfrac{6}{26}\right)\right]+\dfrac{6}{7}:\left[\dfrac{1}{10}+\left(-\dfrac{16}{10}\right)\right]\)
=\(\dfrac{6}{7}:\left(-\dfrac{3}{26}\right)+\dfrac{6}{7}:\left(-\dfrac{3}{2}\right)\)
=\(\dfrac{6}{7}:\left[\left(-\dfrac{3}{26}\right)+\left(-\dfrac{39}{26}\right)\right]\)
=\(\dfrac{6}{7}:\left(-\dfrac{21}{13}\right)\)
=\(-\dfrac{26}{49}\)
TG
27 tháng 6 2020
a) \(-\frac{9}{13}.\frac{12}{29}-\frac{9}{13}.\frac{17}{29}+\frac{24}{13}\)
\(=-\frac{9}{13}\left(\frac{12}{29}+\frac{17}{29}\right)+\frac{24}{13}\)
\(=-\frac{9}{13}+\frac{24}{13}=\frac{15}{13}\)
b)\(\left(\frac{5}{3}-\frac{2}{11}\right):\frac{49}{33}+\left(-\frac{3}{7}\right)^2-\left|\frac{1}{7}-\frac{1}{14}\right|\)
\(=\left(\frac{5}{3}-\frac{2}{11}\right).\frac{33}{49}+\frac{9}{49}-\left|\frac{2}{14}-\frac{1}{14}\right|\)
\(=\frac{49}{33}.\frac{33}{49}+\frac{9}{49}-\frac{1}{14}\)
\(=1+\frac{9}{49}-\frac{1}{14}=\frac{49}{49}+\frac{9}{49}-\frac{1}{14}\)
\(=\frac{58}{49}-\frac{1}{14}=\frac{109}{98}\)
14 tháng 10 2021
\(\left\{{}\begin{matrix}a=\dfrac{35}{49}=\dfrac{5}{7}\\b=\sqrt{\dfrac{5^2}{7^2}}=\dfrac{5}{7}\\c=\dfrac{\sqrt{5^2}+\sqrt{35^2}}{\sqrt{7^2}+\sqrt{49^2}}=\dfrac{5+35}{7+49}=\dfrac{5}{7}\\d=\dfrac{\sqrt{5^2}-\sqrt{35^2}}{\sqrt{7^2}-\sqrt{49^2}}=\dfrac{5-35}{7-49}=\dfrac{5}{7}\end{matrix}\right.\)
\(\Rightarrow a=b=c=d=\dfrac{5}{7}\)
14 tháng 10 2021
\(a=\dfrac{35}{49};b=\dfrac{5}{7}\\ c,=\dfrac{5+35}{7+49}=\dfrac{12}{14}=\dfrac{6}{7}\\ d,=\dfrac{5-35}{7-49}\)
Áp dụng t/c dtsbn:
\(\dfrac{5}{7}=\dfrac{35}{49}=\dfrac{5+35}{7+49}=\dfrac{5-35}{7-49}\) hay \(a=b=c=d\)
KA
9 tháng 9 2017
a,16;22
b,31;43
c,121;169
d,22223;222223
e,31;57
g,782;3907
h,46;64
i,78;108
9 tháng 9 2017
a. 1, 2, 4, 7, 11,16;22
Tổng quát:Số liền sau bằng số liền trước cộng lần lượt với 1;2;3;...
b. 1, 3, 7, 13, 21;31;43
Tổng quát:Số liền sau bằng số liền trước cộng lần lượt với 2;4;6;...
c. 1, 9, 25, 49, 81;121;169
Tổng quát :Số liền sau bằng bình phương số thứ tự của số hạng
d. 1, 3, 23, 223, 2223;22223;222223;...
Các câu sau tương tự
Lười :))
NM
3
N
17 tháng 10 2018
\(=\frac{9^{15}.6^{30}}{27^{21}.8^{11}}\)
\(=\frac{\left(3^2\right)^{15}.3^{30}.2^{30}}{\left(3^3\right)^{21}.\left(2^3\right)^{11}}\)
\(=\frac{3^{30}.3^{30}.2^{30}}{3^{63}.2^{33}}\)
\(=\frac{3^{60}.2^{30}}{2^{63}.3^{33}}=\frac{1}{2^3.3^3}=\frac{1}{216}\)
làm mẫu một bài còn lại tương tự nha bn =)
17 tháng 10 2018
\(\frac{9^{15}.6^{30}}{27^{21}.8^{11}}=\frac{\left(3^2\right)^{15}.\left(2.3\right)^{30}}{\left(3^3\right)^{21}.\left(2^3\right)^{11}}=\frac{3^{60}.2^{30}}{3^{63}.2^{33}}=\frac{1}{3^3.2^3}\)
\(\frac{45^{12}.49^7}{35^{13}.27^8}=\frac{\left(5.3^2\right)^{12}.\left(7^2\right)^7}{\left(5.7\right)^{13}.\left(3^3\right)^8}=\frac{5^{12}.3^{24}.7^{14}}{5^{13}.7^{13}.3^{24}}=\frac{7}{5}\)
#
\(\dfrac{49^5+49^7+49^9}{7^{11}+7^{13}+7^{15}+7^{17}+7^{19}+7^{21}}\)
\(=\dfrac{7^{10}+7^{14}+7^{18}}{7^{11}\left(1+7^2\right)+7^{15}\left(1+7^2\right)+7^{19}\left(1+7^2\right)}\)
\(=\dfrac{7^{10}\left(1+7^4+7^8\right)}{7^{11}\left(1+7^2\right)\left(1+7^4+7^8\right)}=\dfrac{1}{7\left(1+7^2\right)}=\dfrac{1}{7\cdot50}=\dfrac{1}{350}\)