Rút gọn biểu thức:
a)\(\sqrt{\frac{25}{81}\cdot\frac{16}{49}\cdot\frac{169}{9}}\)
b) \(\sqrt{3\frac{1}{16}\cdot2\frac{14}{25}\cdot2\frac{34}{81}}\)
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27 tháng 12 2016
a) \(\left|\frac{-15}{6}\right|-\left|\frac{3}{18}\right|.\sqrt{81}+\sqrt{\frac{9}{64}}\)
\(=\frac{15}{6}-\frac{1}{6}.9+\frac{3}{8}\)
\(=\frac{15}{6}-\frac{9}{6}+\frac{3}{8}\)
\(=1+\frac{3}{8}\)
\(=\frac{11}{8}\)
b) \(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}=\frac{\left(2.3\right)^{15}.\left(3^2\right)^{10}}{3^{34}.2^{13}}=\frac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}=2^2.3=12\)
AT
27 tháng 12 2016
a/ \(\left|\frac{-15}{6}\right|-\left|\frac{3}{18}\right|.\sqrt{81}+\sqrt{\frac{9}{64}}\)
= \(\frac{15}{6}-\frac{3}{18}.9+\frac{8}{8}\)
= \(\frac{15}{6}-\frac{3}{2}+\frac{3}{8}\)
= \(\frac{60-36+9}{24}=\frac{33}{24}=\frac{11}{8}\)
b/ \(\frac{6^{15}.9^{10}}{3^{34}.2^{13}}=\frac{\left(2.3\right)^{15}.\left(3^2\right)^{10}}{3^{34}.2^{13}}\) \(=\frac{2^{15}.3^{15}.3^{20}}{3^{34}.2^{13}}=\frac{2^2.3^{35}}{3^{34}}=\frac{4.3}{1}=12\)
HT
18 tháng 6 2016
\(a,9.3^3.\frac{1}{81}.3^2=3^2.3^3.3^{\left(-4\right)}.3^2=3^{2+3-4+2}=3^3.\)
\(b,4.2^5:\left(2^3.\frac{1}{16}\right)=2^2.2^5:\left(2^3.2^{-4}\right)=2^{2+5}:2^{3-4}=2^7:2^{-1}=2^{7-\left(-1\right)}=2^8.\)
\(c,3^2.2^5.\left(\frac{2}{3}\right)^2=3^2.2^5.\frac{2^2}{3^2}=\left(\frac{3^2}{3^2}\right).\left(2^5.2^2\right)=1.2^{5+2}=2^7\)
\(d,\left(\frac{1}{3}\right)^2.\frac{1}{3}.9^2=\left(\frac{1}{3}\right)^2.\frac{1}{3}.\left(3^2\right)^2=\left(\frac{1}{3}\right)^{2+1}.3^4=\left(\frac{1}{3}\right)^3.\left(\frac{1}{3}\right)^{-4}=\left(\frac{1}{3}\right)^{3-4}=\left(\frac{1}{3}\right)^{-1}=3^1\)
18 tháng 2 2017
\(A=\frac{3}{4}\times\frac{8}{9}\times\frac{15}{16}\times\frac{24}{25}\times...\times\frac{899}{900}\)
\(=\frac{1.3}{2.2}\times\frac{2.4}{3.3}\times\frac{3.5}{4.4}\times...\times\frac{29.31}{30.30}\)
\(=\frac{\left(1\times2\times3\times...\times29\right)\left(3\times4\times5\times...\times31\right)}{\left(2\times3\times4\times...\times30\right)\left(2\times3\times4\times...\times30\right)}\)
\(=\frac{1\times2\times3\times...\times29}{2\times3\times4\times...\times30}.\frac{3\times4\times5\times...\times31}{2\times3\times4\times...\times30}\)
\(=\frac{1}{30}.\frac{31}{2}\)
\(=\frac{31}{60}\)
NT
19 tháng 2 2017
\(A=\frac{3}{4}.\frac{8}{9}.\frac{15}{16}....\frac{899}{900}\\ =\frac{1.3}{2.2}.\frac{2.4}{3.3}.\frac{3.5}{4.4}....\frac{29.31}{30.30}\\ =\frac{1.2.3.4....29}{2.3.4...30}.\frac{3.4.5...31}{2.3.4...30}\\ =\frac{1}{30}.\frac{31}{2}=\frac{31}{60}\)
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a) \(\sqrt{\frac{25}{81}\cdot\frac{16}{49}\cdot\frac{169}{9}}\\ =\sqrt{\left(\frac{5}{9}\right)^2\cdot\left(\frac{4}{7}\right)^2\cdot\left(\frac{13}{3}\right)^2}\\ =\sqrt{\left(\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{13}{3}\right)^2}\\ =\frac{5}{9}\cdot\frac{4}{7}\cdot\frac{13}{3}\\ =\frac{260}{189}\)
b) \(\sqrt{3\frac{1}{6}\cdot2\frac{14}{25}\cdot2\frac{34}{81}}\\ =\sqrt{\frac{19}{6}\cdot\frac{64}{25}\cdot\frac{196}{81}}\\ =\sqrt{\frac{19}{6}\cdot\left(\frac{8}{5}\right)^2\cdot\left(\frac{14}{9}\right)^2}\\ =\sqrt{\frac{19}{6}\cdot\left(\frac{8}{5}\cdot\frac{14}{9}\right)^2}\\ =\sqrt{\frac{19}{6}\cdot\frac{112}{45}}\\ =\sqrt{\frac{1064}{135}}\)
Bổ sung câu b :
\(\sqrt{3\frac{1}{16}.2\frac{14}{25}.2\frac{34}{81}}=\sqrt{\frac{49}{16}.\frac{64}{25}.\frac{196}{81}}=\sqrt{\frac{49}{16}}.\sqrt{\frac{64}{25}}.\sqrt{\frac{196}{81}}=\frac{7}{4}.\frac{8}{5}.\frac{14}{9}=\frac{196}{45}\)