a) \(\left(2x-4\right)\left(x-2\right)^3=0\)

\(\Rightarrow\left[{}\begin{matrix}2x-4=0\\\left(x-2\right)^3=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}2x=4\\x-2-0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=2\\x=2\end{matrix}\right.\)

\(\Rightarrow x=2\)

b) \(3^{x-1}:81=3^3\)

\(\Rightarrow3^{x-1}:3^4=3^3\)

\(\Rightarrow3^{x-1-4}=3^3\)

\(\Rightarrow3^{x-5}=3^3\)

\(\Rightarrow x-5=3\)

\(\Rightarrow x=8\)

c) \(x^{13}=x\)

\(\Rightarrow x^{13}-x=0\)

\(\Rightarrow x\left(x^{12}-1\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{12}-1=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x^{12}=1\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)

d) \(\left(x-9\right)^4=\left(x-9\right)^2\)

\(\Rightarrow\left(x-9\right)^2=x-9\)

\(\Rightarrow\left(x-9\right)^2-\left(x-9\right)=0\)

\(\Rightarrow\left(x-9\right)\left(x-9-1\right)=0\)

\(\Rightarrow\left(x-9\right)\left(x-10\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}x-9=0\\x-10=0\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=9\\x=10\end{matrix}\right.\)

a) \(-\left(-a+c-d\right)-\left(c-a+d\right)\)

\(=a-c+d-c+a-d\)

\(=2a-2c\)

b) \(-\left(a+b-c+d\right)+\left(a-b-c-d\right)\)

\(=-a-b+c-d+a-b-c-d\)

\(=-2b-2d\)

c) \(a\left(b-c-d\right)-a\left(b+c-d\right)\)

\(=ab-ac-ad-ab-ac+ad\)

\(=-2ac\)

d) \(\left(a-b\right)+\left(c-d\right)+\left(a+c\right)-\left(b+d\right)\)

\(=a-b+c-d+a+c-b-d\)

\(=2a-2b+2c-2d\)

4: =4+5+{12+(-8)-(-8)-(-5)+(-12)+16-5+3}

=9+[12+5-12+16-5+3}

=9+19=28

5: =15-[13+8-10-16]-{5-7+9-3}

=15-(-5)-4

=15+5-4

=20-4

=16

m) 63.83-9.7.(-17)

= 5229-63.(-17)

= 5229 - (-1071)

= 5229 + 1071

= 6300

n) 42.3 - 7[(-34)+18]

= 126 - 7. (-16)

= 126 - (-112)

=126+112

= 238

\(p,71\cdot70+35\cdot\left(-7\right)-13\cdot35\)

\(=4970+\left(-245\right)-455=4725-455=4270\)

\(q,18\cdot\left(23-17\right)-13\cdot\left(23+18\right)\)

\(=18\cdot6-13\cdot41=108-533=-425\)

g: =(32-34)+(36-38)+(40-42)

=(-2)+(-2)+(-2)

=-6

l: =-5-{-[7-10]-[5+12]}-[-3+9-4-5]

=-5+(-3)+17-[-3]

=-8+17+3

=20-8=12

9: =>x-2/3=1/5*-7/15=-7/75

=>x=-7/75+50/75=43/75

11: =>x-4/5=3/10*(-7)/3=-7/10

=>x=-7/10+4/5=8/10-7/10=1/10

12:=>7/5*9+x=4/9

=>x=4/9-63/5=-547/45

10: =>x+5/6=-8/147

=>x=-87/98

\(1,-\dfrac{5}{12}\left(\dfrac{4}{9}+-\dfrac{5}{16}\right)\\ =-\dfrac{5}{12}\left(\dfrac{64}{144}+-\dfrac{45}{144}\right)\\ =-\dfrac{5}{12}.\dfrac{19}{144}\\ =-\dfrac{95}{1728}\\ 2,\left(-0,75+\dfrac{1}{2}\right)\left(\dfrac{1}{3}-\dfrac{1}{4}\right)\\ =\left(-\dfrac{3}{4}+\dfrac{1}{2}\right)\left(\dfrac{4}{12}-\dfrac{3}{12}\right)\\ =\left(-\dfrac{3}{4}+\dfrac{2}{4}\right).\dfrac{1}{12}\\ =-\dfrac{1}{4}.\dfrac{1}{12}\\ =-\dfrac{1}{48}\\ 3,-\dfrac{5}{7}.\dfrac{4}{13}+-\dfrac{5}{7}.\dfrac{9}{13}+-\dfrac{5}{7}\\ =-\dfrac{5}{7}.\dfrac{4}{13}+-\dfrac{5}{7}.\dfrac{9}{13}+-\dfrac{5}{7}.1=-\dfrac{5}{7}\left(\dfrac{4}{13}+\dfrac{9}{13}+1\right)\\ =-\dfrac{5}{7}\left(\dfrac{4}{13}+\dfrac{9}{13}+\dfrac{13}{13}\right)\\ =-\dfrac{5}{7}.\dfrac{26}{13}\\ =-\dfrac{5}{7}.2\\ =-\dfrac{10}{7}\)

\(b,4\dfrac{1}{2}x-\dfrac{1}{2}x=\dfrac{2}{3}:\dfrac{4}{9}\\ \dfrac{9}{2}x-\dfrac{1}{2}x=\dfrac{3}{2}\\ \left(\dfrac{9}{2}-\dfrac{1}{2}\right)x=\dfrac{3}{2}\\ 4x=\dfrac{3}{2}\\ x=\dfrac{3}{2}:4\\ x=\dfrac{3}{8}\)