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Bài làm
\(a,\left(\frac{3}{7}+\frac{1}{2}\right)^2\)
\(=\left(\frac{3}{7}\right)^2+\left(\frac{1}{2}\right)^2\)
\(=\frac{9}{49}+\frac{1}{4}\)
\(=\frac{36}{196}+\frac{49}{196}\)
\(=\frac{85}{196}\)
\(b,\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
\(=\left(-\frac{1}{12}\right)^2\)
\(=\frac{1}{144}\)
\(c,\frac{5^4.20^4}{25^5.4^5}\)
\(=\frac{5^4.\left(5.4\right)^4}{\left(5.5\right)^5.4^5}\)
\(=\frac{5^4.5^4.4^4}{5^5.5^5.4^5}\)
\(=\frac{1}{5.5.4}\)
\(=\frac{1}{100}\)
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# Học tốt #
\(a,\left(\frac{3}{7}+\frac{1}{2}\right)^2\)
\(< =>\left(\frac{6}{14}+\frac{7}{14}\right)^2\)
\(< =>\left(\frac{13}{14}\right)^2\)
\(< =>\frac{169}{196}\)
\(b,\left(\frac{3}{4}-\frac{5}{6}\right)^2\)
\(< =>\left(\frac{9}{12}-\frac{10}{12}\right)^2\)
\(< =>\left(\frac{-1}{12}\right)^2\)
\(< =>\frac{-1}{144}\)
\(c,\frac{5^4\cdot20^4}{25^5\cdot4^5}\)
\(< =>\frac{25^2\cdot\left(4\right)^4\cdot\left(5\right)^4}{25^5\cdot4^5}\)
\(< =>\frac{1\cdot1\cdot\left(5\right)^4}{25^3\cdot4}\)
\(< =>\frac{1\cdot25^2}{25^3\cdot4}\)
\(< =>\frac{1}{25\cdot4}\)
\(< =>\frac{1}{100}\)
a, \(\frac{169}{196}\)
b, \(\frac{1}{144}\)
c, \(\frac{1}{100}\)
d, \(\frac{-2560}{3}\)
\(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{13}{14}\right)^2=\frac{169}{196}\)
\(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(-\frac{1}{12}\right)^2=\frac{1}{144}\)
\(\frac{5^4.20^4}{25^5.4^5}=\frac{5^8.2^8}{5^{10}.42^{10}}=\frac{1}{100}\)
\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\left[\left(-\frac{10}{3}\right).\left(-\frac{6}{5}\right)\right]^4.\left(-\frac{10}{3}\right)=4^4.\left(-\frac{10}{3}\right)=-\frac{2560}{3}\)
a. \(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{6+7}{14}\right)^2=\left(\frac{13}{14}\right)^2=\frac{13^2}{14^2}=\frac{169}{196}\)
b. \(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(\frac{9-10}{12}\right)^2=\left(-\frac{1}{12}\right)^2=\frac{\left(-1\right)^2}{12^2}=\frac{1}{144}\)
c. \(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{1}{100}\)
d.\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{\left(-10\right)^5}{3^5}.\frac{\left(-6\right)^4}{5^4}=\frac{\left(-2.5\right)^5.\left(-2.3\right)^4}{3^5.5^4}=\frac{\left(-2\right)^5.5^5.\left(-2\right)^4.3^4}{3^5.5^4}=\frac{\left(-2\right)^9.5}{3}=\frac{-512.5}{3}=-\frac{2560}{3}\)
a, \(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{6}{14}+\frac{7}{14}\right)^2=\left(\frac{13}{14}\right)^2=\frac{169}{196}\)
b, \(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(\frac{9}{12}-\frac{10}{12}\right)^2=\left(-\frac{1}{12}\right)^2=\frac{1}{144}\)
c, \(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^5}=\frac{100^4}{100^5}=\frac{100^4}{100^4.100}=\frac{1}{100}\)
d, \(\left(\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\left(\frac{10}{3}\right)^4.\frac{10}{3}.\left(-\frac{6}{5}\right)^4=\left(\frac{10}{3}.-\frac{6}{5}\right)^4.\frac{10}{3}=\left(-4\right)^4.\frac{10}{3}=256.\frac{10}{3}=853\frac{1}{3}\)
a) \(\left(\frac{3}{7}+\frac{1}{2}\right)^2=\left(\frac{6}{14}+\frac{7}{14}\right)^2=\left(\frac{13}{14}\right)^2=\frac{169}{196}\)
b) \(\left(\frac{3}{4}-\frac{5}{6}\right)^2=\left(\frac{9}{12}-\frac{10}{12}\right)^2=\left(-\frac{1}{2}\right)^2=\frac{1}{4}\)
d) \(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=-\frac{2560}{3}\)
e) \(\left(1+\frac{2}{3}-\frac{1}{4}\right).\left(\frac{4}{5}-\frac{3}{4}\right)^2=\frac{17}{12}.\left(\frac{1}{20}\right)^2=\frac{17}{12}.\frac{1}{400}=\frac{17}{4800}\)
f) \(2:\left(\frac{1}{2}-\frac{2}{3}\right)^3=2:\left(-\frac{1}{6}\right)^3=2:-\frac{1}{216}=-432\)
a) \(x^2-2=\frac{1}{4}\)
\(\Rightarrow x^2=\frac{1}{4}+2\)
\(\Rightarrow x^2=\frac{9}{4}=2,25=1,5^2\)
\(\Rightarrow x=1,5\)
b) \(-\frac{3}{2}.\left(\frac{4}{5}+x\right)=1\frac{3}{2}\)
\(\Rightarrow-\frac{3}{2}.\left(\frac{4}{5}+x\right)=\frac{5}{2}\)
\(\Rightarrow\frac{4}{5}+x=\frac{5}{2}:-\frac{3}{2}\)
\(\Rightarrow\frac{4}{5}+x=-\frac{5}{3}\)
\(\Rightarrow x=-\frac{5}{3}-\frac{4}{5}\)
\(\Rightarrow x=-\frac{37}{15}\)
a. \(\frac{5^4.20^4}{25^5.4^5}=\frac{\left(5.20\right)^4}{\left(25.4\right)^4}=\frac{100^4}{100^5}=\frac{1}{100}\)
b. \(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{\left(-10\right)^5}{3^5}.\frac{\left(-6\right)^4}{5^4}=\frac{\left(-2.5\right)^5.\left(-2.3\right)^4}{3^5.5^4}=\frac{\left(-2\right)^5.5^5.\left(-2\right)^4.3^4}{3^5.5^4}=\frac{\left(-2\right)^9.5^5.3^4}{3^5.5^4}=\frac{\left(-2\right)^9.5}{3}=\frac{-512.5}{3}=\frac{-2560}{3}=\)