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12 tháng 12 2016
\(\left(\frac{3}{7}\right)^{20}\div\left(\frac{9}{49}\right)^5=\left(\frac{3}{7}\right)^{20}\div\left[\left(\frac{3}{7}\right)^2\right]^5\)
\(=\left(\frac{3}{7}\right)^{20}\div\left(\frac{3}{7}\right)^{10}=\left(\frac{3}{7}\right)^{10}\)
17 tháng 9 2020
a) \(4\frac{5}{9}:\left(-\frac{5}{7}\right)+\frac{49}{9}:\left(-\frac{5}{7}\right)=\frac{41}{9}:\left(-\frac{5}{7}\right)+\frac{49}{9}:\left(-\frac{5}{7}\right)\)
\(=\frac{41}{9}\cdot\left(-\frac{7}{5}\right)+\frac{49}{9}\cdot\left(-\frac{7}{5}\right)=\left(\frac{41}{9}+\frac{49}{9}\right)\cdot\left(-\frac{7}{5}\right)=10\cdot\left(-\frac{7}{5}\right)=-14\)
b) \(\left(\frac{-3}{5}+\frac{4}{9}\right):\frac{7}{11}+\left(\frac{-2}{5}+\frac{5}{9}\right):\frac{7}{11}\)
\(=\left(\frac{-3}{5}+\frac{4}{9}+\frac{-2}{5}+\frac{5}{9}\right):\frac{7}{11}\)
\(=\left(\frac{-3}{5}+\frac{-2}{5}+\frac{4}{9}+\frac{5}{9}\right):\frac{7}{11}\)
\(=\left(-1+1\right):\frac{7}{11}=0\cdot\frac{11}{7}=0\)
c) \(\left(\frac{3}{4}\right)^4\cdot\left(\frac{8}{9}\right)^2=\left(\frac{3}{4}\right)^2\cdot\left(\frac{3}{4}\right)^2\cdot\left(\frac{8}{9}\right)^2=\left(\frac{3}{4}\cdot\frac{3}{4}\cdot\frac{8}{9}\right)^2\)
\(=\left(\frac{1}{2}\right)^2=\frac{1}{4}\)
d) \(\left(-\frac{3}{5}\right)^6\cdot\left(-\frac{5}{3}\right)^5=\left(-\frac{3}{5}\right)^5\cdot\left(-\frac{3}{5}\right)\cdot\left(-\frac{5}{3}\right)^5=\left[\left(-\frac{3}{5}\right)\cdot\left(-\frac{5}{3}\right)\right]^5\cdot\left(-\frac{3}{5}\right)\)
\(=1^5\cdot\left(-\frac{3}{5}\right)=1\cdot\left(-\frac{3}{5}\right)=-\frac{3}{5}\)
e) \(\frac{8^{14}}{4^4\cdot64^5}=\frac{\left(2^3\right)^{14}}{\left(2^2\right)^4\cdot\left(2^6\right)^5}=\frac{2^{42}}{2^8\cdot2^{30}}=\frac{2^{42}}{2^{38}}=2^4=16\)
f) \(\frac{9^{10}\cdot27^7}{81^7\cdot3^{15}}=\frac{\left(3^2\right)^{10}\cdot\left(3^3\right)^7}{\left(3^4\right)^7\cdot3^{15}}=\frac{3^{20}\cdot3^{21}}{3^{28}\cdot3^{15}}=\frac{3^{41}}{3^{43}}=3^{-2}=\frac{1}{3^2}=\frac{1}{9}\)
PT
1
4 tháng 12 2016
\(\left(\frac{3}{7}\right)^{20}:\left(\frac{9}{49}\right)^5\)
\(=\left[\left(\frac{3}{7}\right)^2\right]^{10}:\left[\left(\frac{3}{7}\right)^2\right]^5\)
\(=\left[\left(\frac{3}{7}\right)^2\right]^5\)
\(=\left(\frac{3}{7}\right)^{10}\)
BT
29 tháng 7 2018
\(a.\left(\frac{2}{5}\right)^5:\left(\frac{9}{25}\right)^5=\left(\frac{2\cdot25}{9\cdot5}\right)^5=\frac{10}{9}^5\)
\(b.25\cdot5^3\cdot\frac{1}{625}\cdot5^2=\frac{5^7}{5^4}=5^3\)
\(c.\frac{20^5\cdot5^{10}}{100^5}=\frac{2^{10}\cdot5^{15}}{2^{10}\cdot5^{10}}=5^5\)
\(d.\frac{1}{7}^2\cdot\frac{1}{7}\cdot49^2=\frac{7^4}{7^3}=7\)
S
14 tháng 7 2016
a) \(25^3:5^2=5^6:5^2=5^4=625\)
b) \(\left(\frac{3}{7}\right)^{21}:\left(\frac{9}{49}\right)^6=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{12}=\left(\frac{3}{7}\right)^9\)
c) \(3-\left(-\frac{6}{7}\right)^0+\left(\frac{1}{2}\right)^2:2=3-1+\frac{1}{8}=\frac{17}{8}\)
30 tháng 7 2018
a) \(\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}^3\right)^6\)
\(=\left(\frac{3}{7}\right)^{21}:\left(\frac{3}{7}\right)^{18}\)
\(=\left(\frac{3}{7}\right)^{21-18}\)
\(=\left(\frac{3}{7}\right)^3\)
\(=\frac{27}{343}\)
17 tháng 8 2017
\(a,\left(\frac{3}{7}\right)^{24}:\left(\frac{9}{49}\right)^6\)
\(=\frac{3^{24}}{7^{24}}.\frac{49^6}{9^6}\)
\(=\frac{3^{24}}{7^{24}}.\frac{7^{12}}{3^{12}}\)
\(=\frac{3^{12}}{7^{12}}\)\(=\left(\frac{3}{7}\right)^{12}\)
\(b,3^2.2^5.\left(\frac{2}{3}\right)^2\)
\(=3^2.2^5.\frac{2^2}{9}\)
\(=2^5.2^2\)
\(=2^7\)
\(c,\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2\)
\(=\left(\frac{1}{3}\right)^3.9^2\)
\(=\frac{1.81}{27}\)
\(=3\)
0.000209041
Bài làm
\(\left(\frac{3}{7}\right)^{20}:\left(\frac{9}{49}\right)^5\)
= \(\left(\frac{3}{7}\right)^{20}:\left(\frac{3}{7}^2\right)^5\)
= \(\left(\frac{3}{7}\right)^{20}:\left(\frac{3}{7}\right)^{10}\)
= \(\left(\frac{3}{7}\right)^{20-10}\)
= \(\left(\frac{3}{7}\right)^{10}\)
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