\(a,\dfrac{2}{3}-\dfrac{5}{6}+\dfrac{3}{4}\)

\(=(\dfrac{2}{3}+\dfrac{3}{4})-\dfrac{5}{6}\)

\(=\dfrac{7}{12}\)

\(b,\dfrac{6}{7}.\dfrac{8}{13}+\dfrac{6}{13}.\dfrac{9}{7}-\dfrac{-4}{13}.\dfrac{6}{7}\)

\(=\dfrac{6}{7}.(\dfrac{8}{13}-\dfrac{4}{13})+(\dfrac{6}{13}.\dfrac{9}{7})\)

\(=(\dfrac{6}{7}.\dfrac{4}{13})+\dfrac{54}{91}\)

\(=\dfrac{24}{91}+\dfrac{54}{91}\)

\(=\dfrac{78}{91}=\dfrac{6}{7}\)

\(c,19.(-26)\)

\(=-494\)

a) `2/3 - 5/6 +3/4`

`=4/6-5/6+3/4`

`=-1/6+3/4`

`=-4/24+18/24`

`=14/24=7/12`

b) `6/7 .8/13 +6/13 .9/7 -4/13 .6/7`

`=6/7 .(8/13-4/13) + 6/13 .9/7`

`=6/7 . 4/13 + 6/13 . 9/7`

`= 6/13 .4/7 +6/13 .9/7`

`=6/13 . (4/7+9/7)`

`=6/13 . 13/7`

`=6/7`

c) `19.(-26)`

`=(1-20).(20+6)`

`=20+6-400-120`

`=-494`

Lời giải:
a.

$-18: \frac{3}{5}=-18.\frac{5}{3}=-30$

b.

$\frac{3}{4}:(-9)=\frac{3}{4}.\frac{-1}{9}=\frac{-1}{12}$

c.

$\frac{13}{20}-\frac{6}{7}: \frac{10}{21}=\frac{13}{20}-\frac{6}{7}.\frac{21}{10}$

$=\frac{13}{20}-\frac{9}{5}=\frac{13}{20}-\frac{36}{20}=\frac{-23}{20}$

d.

$\frac{-21}{5}: (\frac{7}{3}.\frac{7}{5})=\frac{-21}{5}: \frac{49}{15}$

$=\frac{-21}{5}.\frac{15}{49}=\frac{-9}{7}$

e.

$(\frac{-2}{5}+\frac{1}{4}): (1-\frac{2}{5})$

$=\frac{-3}{20}: \frac{3}{5}=\frac{-1}{4}$

\(\dfrac{8^{14}}{4^4.64^5}=\dfrac{\left(2^3\right)^{14}}{\left(2^2\right)^4.\left(2^5\right)^5}=\dfrac{2^{42}}{2^8.2^{25}}=2^{42-\left(8+25\right)}=2^9\)

\(\dfrac{9^{10}.27^7}{81^7.3^{15}}=\dfrac{\left(3^2\right)^{10}.\left(3^3\right)^7}{\left(3^4\right)^7.3^{15}}=\dfrac{3^{20}.3^{21}}{3^{28}.3^{15}}=\dfrac{3^{20+21}}{3^{28+15}}=\dfrac{3^{41}}{3^{41}.3^2}=\dfrac{1}{3^2}=\dfrac{1}{9}\)

a. \(\dfrac{5}{17}+\dfrac{-5}{34}.\dfrac{2}{5}\)

=   \(\dfrac{5}{17}+\dfrac{1}{-17}\)

=    \(\dfrac{5}{17}+\dfrac{-1}{17}\)

=     \(\dfrac{4}{17}\)

b. \(\dfrac{1}{2}.\dfrac{5}{6}+\dfrac{2}{3}.\dfrac{3}{4}\)

= \(\dfrac{5}{12}+\dfrac{1}{2}\)

= \(\dfrac{5}{12}+\dfrac{6}{12}\)

= \(\dfrac{11}{12}\)

c. \(\left(\dfrac{-2}{5}+\dfrac{1}{3}\right).\left(\dfrac{3}{2}-\dfrac{3}{7}\right)\)

= \(\left(\dfrac{-6}{15}+\dfrac{5}{15}\right).\left(\dfrac{21}{14}-\dfrac{6}{14}\right)\)

= \(\dfrac{-1}{15}.\dfrac{15}{14}\)

= \(\dfrac{-1}{14}\)

d. \(\left(1+\dfrac{1}{2}\right).\left(1+\dfrac{1}{3}\right).\left(1+\dfrac{1}{4}\right)\)

= \(\left(\dfrac{2}{2}+\dfrac{1}{2}\right).\left(\dfrac{3}{3}+\dfrac{1}{3}\right).\left(\dfrac{4}{4}+\dfrac{1}{4}\right)\)

= \(\dfrac{3}{2}.\dfrac{4}{3}.\dfrac{5}{4}\)

= \(\dfrac{5}{2}\)

a: \(=\dfrac{5}{34}\cdot\dfrac{2}{5}=\dfrac{2}{34}=\dfrac{1}{17}\)

b: \(=\dfrac{5}{12}+\dfrac{6}{12}=\dfrac{11}{12}\)

c: \(=\dfrac{-6+5}{15}\cdot\dfrac{21-6}{15}=-\dfrac{1}{15}\)

Thực hiện phép tính:

a, 5/17 + -5/34 . 2/5=5/17 + -1/17=4/17

b, 1/2 . 5/6 + 2/3 . 3/4 =5/12 + 6/12 =11/12

c, ( -2/5 + 1/3 ) . ( 3/2 - 3/7 )=-1/15 . 15/14=1/14