a; 

c; \(\dfrac{1}{10}\) + \(\dfrac{4}{20}\) + \(\dfrac{9}{30}\)+\(\dfrac{16}{40}+\dfrac{25}{50}+\dfrac{36}{60}+\dfrac{49}{70}+\dfrac{64}{80}+\dfrac{81}{90}\)

= \(\dfrac{1}{10}+\dfrac{2}{10}+\dfrac{3}{10}+\dfrac{4}{10}+\dfrac{5}{10}+\dfrac{6}{10}+\dfrac{7}{10}+\dfrac{8}{10}+\dfrac{9}{10}\)

= \(\dfrac{1+2+3+4+5+6+7+8+9}{10}\)

=  \(\dfrac{\left(1+9\right)+\left(2+8\right)+\left(3+7\right)+\left(4+6\right)+5}{10}\)

= \(\dfrac{10+10+10+10+5}{10}\)

= \(\dfrac{\left(10+10+10+10\right)+5}{10}\)

= \(\dfrac{10\times4+5}{10}\)

= \(\dfrac{45}{10}\)

= \(\dfrac{9}{2}\)

\(\frac{8}{9}:\frac{4}{3}\times\frac{5}{8}=\frac{8}{9}\times\frac{3}{4}\times\frac{5}{8}=\frac{2}{3}\times\frac{5}{8}=\frac{5}{12}\)

~HT~

\(\frac{14}{7}\):\(\frac{7}{34}\)x\(\frac{1}{8}\)

=\(\frac{14}{7}\)x\(\frac{34}{7}\)x\(\frac{1}{8}\)

=2x\(\frac{34}{7}\)x\(\frac{1}{8}\)

=\(\frac{68}{7}\)x\(\frac{1}{8}\)

=\(\frac{68}{56}\)=\(\frac{37}{28}\)

Hok tốt!

a)

\({5^7}{.5^5} = 5^{7+5}={5^{12}}\)

\({9^5} :{8^0} = {9^5}:1 = {9^5}\)

\(2^{10}:64.16 = 2^{10}:2^6.2^4 = 2^{10-6+4} = 2^8\)

b)

\(\begin{array}{l}54297 = 5.10000 + 4.1000 + 2.100 + 9.10 + 7\\ = {5.10^4} + {4.10^3} + {2.10^2} + 9.10 + 7\end{array}\)

\(\begin{array}{l}2023 = 2.1000 +0.100+2.10 + 3\\ = {2.10^3}+ 2.10 +3\end{array}\)

`a) 1/2 + 1/4 + 1/5`
`=10/20 + 5/20 + 4/20`
`= 19/20`

`b)1/2xx 4/5 : 1/4`
`= 4/10 : 1/4`
`= 8/5`

\(a\)/ \(\dfrac{1}{2}+\dfrac{1}{4}-\dfrac{1}{5}=\dfrac{11}{20}\)

\(b\)/ \(\dfrac{1}{2}.\dfrac{4}{5}:\dfrac{1}{4}=\dfrac{8}{5}\)