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, \(\frac{169}{196}\)

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.\(\left(-\frac{10}{3}\right)^5.\left(-\frac{6}{5}\right)^4=\frac{\left(-10\right)^5}{3^5}.\frac{\left(-6\right)^4}{5^4}=\frac{\left(-2.5\right)^5.\left(-2.3\right)^4}{3^5.5^4}=\frac{\left(-2\right)^5.5^5.\left(-2\right)^4.3^4}{3^5.5^4}=\frac{\left(-2\right)^9.5}{3}=\frac{-512.5}{3}=-\frac{2560}{3}\)

Bài làm

\(a,\left(\frac{3}{7}+\frac{1}{2}\right)^2\)

\(=\left(\frac{3}{7}\right)^2+\left(\frac{1}{2}\right)^2\)

\(=\frac{9}{49}+\frac{1}{4}\)

\(=\frac{36}{196}+\frac{49}{196}\)

\(=\frac{85}{196}\)

\(b,\left(\frac{3}{4}-\frac{5}{6}\right)^2\)

\(=\left(-\frac{1}{12}\right)^2\)

\(=\frac{1}{144}\)

\(c,\frac{5^4.20^4}{25^5.4^5}\)

\(=\frac{5^4.\left(5.4\right)^4}{\left(5.5\right)^5.4^5}\)

\(=\frac{5^4.5^4.4^4}{5^5.5^5.4^5}\)

\(=\frac{1}{5.5.4}\)

\(=\frac{1}{100}\)

~ Check đúng cho minh nha. ~

# 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,(3/7)^2+2.3/7.1/2+(1/2)^2

=9/49+3/7+1/4

=169/196

b,(3/4)^2-2.3/4.5/6+(5/6)^2

=9/16-5/4+25/36

=1/144

a)

\(\begin{array}{l}\frac{1}{9} - 0,3.\frac{5}{9} + \frac{1}{3}\\ = \frac{1}{9} - \frac{3}{{10}}.\frac{5}{9} + \frac{1}{3}\\ = \frac{1}{9} - \frac{3}{{2.5}}.\frac{5}{{3.3}} + \frac{1}{3}\\ = \frac{1}{9} - \frac{1}{6} + \frac{1}{3}\\ = \frac{2}{{18}} - \frac{3}{{18}} + \frac{6}{{18}}\\ = \frac{5}{{18}}\end{array}\)

b)

\(\begin{array}{l}{\left( {\frac{{ - 2}}{3}} \right)^2} + \frac{1}{6} - {\left( { - 0,5} \right)^3}\\ = \frac{4}{9} + \frac{1}{6} - \left( {\frac{{ - 1}}{2}} \right)^3\\  = \frac{4}{9} + \frac{1}{6} - \left( {\frac{{ - 1}}{8}} \right)\\ = \frac{4}{9} + \frac{1}{6} + \frac{1}{8}\\ = \frac{{32}}{{72}} + \frac{{12}}{{72}} + \frac{9}{{72}}\\ = \frac{{53}}{{72}}\end{array}\)