a: \(A=\dfrac{x^{\dfrac{1}{3}}\cdot y^{\dfrac{1}{2}}+y^{\dfrac{1}{3}}\cdot x^{\dfrac{1}{2}}}{x^{\dfrac{1}{6}}+y^{\dfrac{1}{6}}}=\dfrac{x^{\dfrac{1}{3}}\cdot y^{\dfrac{1}{3}}\left(x^{\dfrac{1}{6}}+y^{\dfrac{1}{6}}\right)}{x^{\dfrac{1}{6}}+y^{\dfrac{1}{6}}}=x^{\dfrac{1}{3}}\cdot y^{\dfrac{1}{3}}=\left(xy\right)^{\dfrac{1}{3}}\)

b: \(B=\dfrac{x^{3+\sqrt{3}}}{y^2}\cdot\dfrac{x^{-\sqrt{3}-1}}{y^{-2}}=\dfrac{x^{3+\sqrt{3}-\sqrt{3}-1}}{y^{2-2}}=x^2\)

\(\frac{10}{25}=\frac{10:5}{25:5}=\frac{2}{5}\)

\(\frac{5}{20}=\frac{5:5}{20:5}=\frac{1}{4}\)

\(\frac{6}{30}=\frac{6:6}{30:6}=\frac{1}{5}\)

\(\frac{60}{20}=\frac{60:20}{20:20}=3\)

a) \(\dfrac{11\cdot8-11\cdot3}{17-6}\)

\(=\dfrac{11\cdot\left(8-3\right)}{11}=5\)

b) \(\dfrac{24-12\cdot13}{12+4\cdot9}\)

\(=\dfrac{12\cdot\left(2-13\right)}{12\left(1+3\right)}=\dfrac{-11}{4}\)

a: \(=\dfrac{21\cdot11}{22\cdot9}=\dfrac{1}{2}\cdot\dfrac{7}{3}=\dfrac{7}{6}\)

b: \(=\dfrac{49\cdot8}{10}=49\cdot\dfrac{4}{5}=\dfrac{196}{5}\)

c: \(=\dfrac{12\cdot\left(-4\right)}{32\cdot6}=\dfrac{-48}{192}=-\dfrac{1}{4}\)

=21⋅1122⋅9=12⋅73=76

a: 12/21=4/7=8/14

4/56=1/14

b: 12/15=4/5=24/30

6/36=1/6=5/30

15/50=3/10=9/30

c: 63/77=9/11=81/99

60/108=5/9=55/99

-18/27=-2/3=-66/99

d: -26/-156=1/6=7/42

49/-14=-7/2=-147/42

32/112=2/7=12/42

$\frac{{15}}{6} = \frac{{15:3}}{{6:3}} = \frac{5}{2}$

$\frac{{12}}{{16}} = \frac{{12:4}}{{16:4}} = \frac{3}{4}$

 $\frac{{35}}{{105}} = \frac{{35:35}}{{105:35}} = \frac{1}{3}$

a: A=(-1)+(-1)+...+(-1)+2023

=2023-1011=1012

\(a,\dfrac{583}{352}=\dfrac{53}{32}\\ b,\dfrac{121212}{313131}=\dfrac{12}{31}\\ c,\dfrac{153.24-153.11}{160-7}=\dfrac{153\left(24-11\right)}{153}=13\)

a.53/32

b.12/31

c.13

a,434343/343434= 43/34                         b,3625/560= 725/112

a,434343/343434= 43/34                         b,3625/560= 725/112

43/34            725/112

a, =5/14

b, = 1/6

c, = 3/2

d, = 8/7

5/14

1/6

3/2

8/7

a,5/14

b,1/6

c,3/2

d,8/7