import re
text = ''
m1 = ['+', '-', '*', '/', ' ']
for i in range(2, 10):
    for j in '+-*/ ':
        m1.append(f'**(1/{i}){j}')
for i in '23456789':
    for j in m1:
        for k in m1:
            for l in m1:
                try:
                    t = f'{i}{j}{i}{k}{i}{l}'
                    if eval(t) == 6:
                        print(f'{t}= 6')
                        text += re.sub(r"(?P<word1>\d+)\*\*\(1/(?P<word2>\d+)\)", '\\\\sqrt[\g<word2>]{\g<word1>}', f'{t}= 6\\\\\n').replace('*', '×').replace('/', '÷').replace('\sqrt[2]', '\sqrt')
                except:
                    pass
text = f'$${text[:-3]}$$'

2+2+2 = 6
2+2*2 = 6
2*2+2 = 6
3+3**(1/2)*3**(1/2) = 6
3*3-3 = 6
3**(1/2)*3**(1/2)+3 = 6
4+4-4**(1/2) = 6
4+4/4**(1/2) = 6
4+4**(1/3)*4**(1/6) = 6
4+4**(1/4)*4**(1/4) = 6
4+4**(1/6)*4**(1/3) = 6
4-4**(1/2)+4 = 6
4*4**(1/2)-4**(1/2) = 6
4/4**(1/2)+4 = 6
4**(1/2)+4**(1/2)+4**(1/2) = 6
4**(1/2)+4**(1/2)*4**(1/2) = 6
4**(1/2)*4-4**(1/2) = 6
4**(1/2)*4**(1/2)+4**(1/2) = 6
4**(1/3)*4**(1/6)+4 = 6
4**(1/4)*4**(1/4)+4 = 6
4**(1/6)*4**(1/3)+4 = 6
5+5/5 = 6
5+5**(1/2)/5**(1/2) = 6
5+5**(1/3)/5**(1/3) = 6
5+5**(1/4)/5**(1/4) = 6
5+5**(1/5)/5**(1/5) = 6
5+5**(1/6)/5**(1/6) = 6
5+5**(1/7)/5**(1/7) = 6
5+5**(1/8)/5**(1/8) = 6
5+5**(1/9)/5**(1/9) = 6
5/5+5 = 6
5**(1/2)/5**(1/2)+5 = 6
5**(1/3)/5**(1/3)+5 = 6
5**(1/4)/5**(1/4)+5 = 6
5**(1/5)/5**(1/5)+5 = 6
5**(1/6)/5**(1/6)+5 = 6
5**(1/7)/5**(1/7)+5 = 6
5**(1/8)/5**(1/8)+5 = 6
5**(1/9)/5**(1/9)+5 = 6
6+6-6 = 6
6+6**(1/3)-6**(1/3) = 6
6+6**(1/4)-6**(1/4) = 6
6+6**(1/5)-6**(1/5) = 6
6+6**(1/6)-6**(1/6) = 6
6+6**(1/7)-6**(1/7) = 6
6+6**(1/8)-6**(1/8) = 6
6+6**(1/9)-6**(1/9) = 6
6-6+6 = 6
6-6**(1/2)+6**(1/2) = 6
6-6**(1/3)+6**(1/3) = 6
6-6**(1/4)+6**(1/4) = 6
6-6**(1/5)+6**(1/5) = 6
6-6**(1/6)+6**(1/6) = 6
6-6**(1/7)+6**(1/7) = 6
6-6**(1/8)+6**(1/8) = 6
6-6**(1/9)+6**(1/9) = 6
6*6/6 = 6
6*6**(1/2)/6**(1/2) = 6
6*6**(1/3)/6**(1/3) = 6
6*6**(1/6)/6**(1/6) = 6
6*6**(1/7)/6**(1/7) = 6
6*6**(1/8)/6**(1/8) = 6
6*6**(1/9)/6**(1/9) = 6
6/6*6 = 6
6/6**(1/2)*6**(1/2) = 6
6/6**(1/3)*6**(1/3) = 6
6/6**(1/4)*6**(1/4) = 6
6/6**(1/5)*6**(1/5) = 6
6/6**(1/6)*6**(1/6) = 6
6/6**(1/7)*6**(1/7) = 6
6/6**(1/8)*6**(1/8) = 6
6/6**(1/9)*6**(1/9) = 6
6**(1/2)-6**(1/2)+6 = 6
6**(1/2)*6/6**(1/2) = 6
6**(1/2)/6**(1/2)*6 = 6
6**(1/3)+6-6**(1/3) = 6
6**(1/3)-6**(1/3)+6 = 6
6**(1/3)*6/6**(1/3) = 6
6**(1/3)*6**(1/3)*6**(1/3) = 6
6**(1/3)*6**(1/6)*6**(1/2) = 6
6**(1/3)/6**(1/3)*6 = 6
6**(1/4)+6-6**(1/4) = 6
6**(1/4)-6**(1/4)+6 = 6
6**(1/4)*6**(1/4)*6**(1/2) = 6
6**(1/4)/6**(1/4)*6 = 6
6**(1/5)+6-6**(1/5) = 6
6**(1/5)-6**(1/5)+6 = 6
6**(1/5)/6**(1/5)*6 = 6
6**(1/6)+6-6**(1/6) = 6
6**(1/6)-6**(1/6)+6 = 6
6**(1/6)*6/6**(1/6) = 6
6**(1/6)*6**(1/3)*6**(1/2) = 6
6**(1/6)/6**(1/6)*6 = 6
6**(1/7)+6-6**(1/7) = 6
6**(1/7)-6**(1/7)+6 = 6
6**(1/7)*6/6**(1/7) = 6
6**(1/7)/6**(1/7)*6 = 6
6**(1/8)+6-6**(1/8) = 6
6**(1/8)-6**(1/8)+6 = 6
6**(1/8)*6/6**(1/8) = 6
6**(1/8)/6**(1/8)*6 = 6
6**(1/9)+6-6**(1/9) = 6
6**(1/9)-6**(1/9)+6 = 6
6**(1/9)*6/6**(1/9) = 6
6**(1/9)/6**(1/9)*6 = 6
7-7/7 = 6
7-7**(1/2)/7**(1/2) = 6
7-7**(1/3)/7**(1/3) = 6
7-7**(1/4)/7**(1/4) = 6
7-7**(1/5)/7**(1/5) = 6
7-7**(1/6)/7**(1/6) = 6
7-7**(1/7)/7**(1/7) = 6
7-7**(1/8)/7**(1/8) = 6
7-7**(1/9)/7**(1/9) = 6
8-8**(1/2)/8**(1/6) = 6
8-8**(1/6)*8**(1/6) = 6
8/8**(1/3)+8**(1/3) = 6
8**(1/2)*8**(1/6)+8**(1/3) = 6
8**(1/3)+8/8**(1/3) = 6
8**(1/3)+8**(1/2)*8**(1/6) = 6
8**(1/3)+8**(1/3)+8**(1/3) = 6
8**(1/3)+8**(1/3)*8**(1/3) = 6
8**(1/3)+8**(1/6)*8**(1/2) = 6
8**(1/3)*8**(1/3)+8**(1/3) = 6
8**(1/6)*8**(1/2)+8**(1/3) = 6
9-9/9**(1/2) = 6
9-9**(1/3)*9**(1/6) = 6
9-9**(1/4)*9**(1/4) = 6
9-9**(1/6)*9**(1/3) = 6
9/9**(1/2)+9**(1/2) = 6
9**(1/2)+9/9**(1/2) = 6
9**(1/2)+9**(1/3)*9**(1/6) = 6
9**(1/2)+9**(1/4)*9**(1/4) = 6
9**(1/2)+9**(1/6)*9**(1/3) = 6
9**(1/2)*9**(1/2)-9**(1/2) = 6
9**(1/3)*9**(1/6)+9**(1/2) = 6
9**(1/4)*9**(1/4)+9**(1/2) = 6
9**(1/6)*9**(1/3)+9**(1/2) = 6

$$2+2+2 = 6\\ 2+2×2 = 6\\ 2×2+2 = 6\\ 3+\sqrt{3}×\sqrt{3} = 6\\ 3×3-3 = 6\\ \sqrt{3}×\sqrt{3}+3 = 6\\ 4+4-\sqrt{4} = 6\\ 4+4÷\sqrt{4} = 6\\ 4+\sqrt[3]{4}×\sqrt[6]{4} = 6\\ 4+\sqrt[4]{4}×\sqrt[4]{4} = 6\\ 4+\sqrt[6]{4}×\sqrt[3]{4} = 6\\ 4-\sqrt{4}+4 = 6\\ 4×\sqrt{4}-\sqrt{4} = 6\\ 4÷\sqrt{4}+4 = 6\\ \sqrt{4}+\sqrt{4}+\sqrt{4} = 6\\ \sqrt{4}+\sqrt{4}×\sqrt{4} = 6\\ \sqrt{4}×4-\sqrt{4} = 6\\ \sqrt{4}×\sqrt{4}+\sqrt{4} = 6\\ \sqrt[3]{4}×\sqrt[6]{4}+4 = 6\\ \sqrt[4]{4}×\sqrt[4]{4}+4 = 6\\ \sqrt[6]{4}×\sqrt[3]{4}+4 = 6\\ 5+5÷5 = 6\\ 5+\sqrt{5}÷\sqrt{5} = 6\\ 5+\sqrt[3]{5}÷\sqrt[3]{5} = 6\\ 5+\sqrt[4]{5}÷\sqrt[4]{5} = 6\\ 5+\sqrt[5]{5}÷\sqrt[5]{5} = 6\\ 5+\sqrt[6]{5}÷\sqrt[6]{5} = 6\\ 5+\sqrt[7]{5}÷\sqrt[7]{5} = 6\\ 5+\sqrt[8]{5}÷\sqrt[8]{5} = 6\\ 5+\sqrt[9]{5}÷\sqrt[9]{5} = 6\\ 5÷5+5 = 6\\ \sqrt{5}÷\sqrt{5}+5 = 6\\ \sqrt[3]{5}÷\sqrt[3]{5}+5 = 6\\ \sqrt[4]{5}÷\sqrt[4]{5}+5 = 6\\ \sqrt[5]{5}÷\sqrt[5]{5}+5 = 6\\ \sqrt[6]{5}÷\sqrt[6]{5}+5 = 6\\ \sqrt[7]{5}÷\sqrt[7]{5}+5 = 6\\ \sqrt[8]{5}÷\sqrt[8]{5}+5 = 6\\ \sqrt[9]{5}÷\sqrt[9]{5}+5 = 6\\ 6+6-6 = 6\\ 6+\sqrt[3]{6}-\sqrt[3]{6} = 6\\ 6+\sqrt[4]{6}-\sqrt[4]{6} = 6\\ 6+\sqrt[5]{6}-\sqrt[5]{6} = 6\\ 6+\sqrt[6]{6}-\sqrt[6]{6} = 6\\ 6+\sqrt[7]{6}-\sqrt[7]{6} = 6\\ 6+\sqrt[8]{6}-\sqrt[8]{6} = 6\\ 6+\sqrt[9]{6}-\sqrt[9]{6} = 6\\ 6-6+6 = 6\\ 6-\sqrt{6}+\sqrt{6} = 6\\ 6-\sqrt[3]{6}+\sqrt[3]{6} = 6\\ 6-\sqrt[4]{6}+\sqrt[4]{6} = 6\\ 6-\sqrt[5]{6}+\sqrt[5]{6} = 6\\ 6-\sqrt[6]{6}+\sqrt[6]{6} = 6\\ 6-\sqrt[7]{6}+\sqrt[7]{6} = 6\\ 6-\sqrt[8]{6}+\sqrt[8]{6} = 6\\ 6-\sqrt[9]{6}+\sqrt[9]{6} = 6\\ 6×6÷6 = 6\\ 6×\sqrt{6}÷\sqrt{6} = 6\\ 6×\sqrt[3]{6}÷\sqrt[3]{6} = 6\\ 6×\sqrt[6]{6}÷\sqrt[6]{6} = 6\\ 6×\sqrt[7]{6}÷\sqrt[7]{6} = 6\\ 6×\sqrt[8]{6}÷\sqrt[8]{6} = 6\\ 6×\sqrt[9]{6}÷\sqrt[9]{6} = 6\\ 6÷6×6 = 6\\ 6÷\sqrt{6}×\sqrt{6} = 6\\ 6÷\sqrt[3]{6}×\sqrt[3]{6} = 6\\ 6÷\sqrt[4]{6}×\sqrt[4]{6} = 6\\ 6÷\sqrt[5]{6}×\sqrt[5]{6} = 6\\ 6÷\sqrt[6]{6}×\sqrt[6]{6} = 6\\ 6÷\sqrt[7]{6}×\sqrt[7]{6} = 6\\ 6÷\sqrt[8]{6}×\sqrt[8]{6} = 6\\ 6÷\sqrt[9]{6}×\sqrt[9]{6} = 6\\ \sqrt{6}-\sqrt{6}+6 = 6\\ \sqrt{6}×6÷\sqrt{6} = 6\\ \sqrt{6}÷\sqrt{6}×6 = 6\\ \sqrt[3]{6}+6-\sqrt[3]{6} = 6\\ \sqrt[3]{6}-\sqrt[3]{6}+6 = 6\\ \sqrt[3]{6}×6÷\sqrt[3]{6} = 6\\ \sqrt[3]{6}×\sqrt[3]{6}×\sqrt[3]{6} = 6\\ \sqrt[3]{6}×\sqrt[6]{6}×\sqrt{6} = 6\\ \sqrt[3]{6}÷\sqrt[3]{6}×6 = 6\\ \sqrt[4]{6}+6-\sqrt[4]{6} = 6\\ \sqrt[4]{6}-\sqrt[4]{6}+6 = 6\\ \sqrt[4]{6}×\sqrt[4]{6}×\sqrt{6} = 6\\ \sqrt[4]{6}÷\sqrt[4]{6}×6 = 6\\ \sqrt[5]{6}+6-\sqrt[5]{6} = 6\\ \sqrt[5]{6}-\sqrt[5]{6}+6 = 6\\ \sqrt[5]{6}÷\sqrt[5]{6}×6 = 6\\ \sqrt[6]{6}+6-\sqrt[6]{6} = 6\\ \sqrt[6]{6}-\sqrt[6]{6}+6 = 6\\ \sqrt[6]{6}×6÷\sqrt[6]{6} = 6\\ \sqrt[6]{6}×\sqrt[3]{6}×\sqrt{6} = 6\\ \sqrt[6]{6}÷\sqrt[6]{6}×6 = 6\\ \sqrt[7]{6}+6-\sqrt[7]{6} = 6\\ \sqrt[7]{6}-\sqrt[7]{6}+6 = 6\\ \sqrt[7]{6}×6÷\sqrt[7]{6} = 6\\ \sqrt[7]{6}÷\sqrt[7]{6}×6 = 6\\ \sqrt[8]{6}+6-\sqrt[8]{6} = 6\\ \sqrt[8]{6}-\sqrt[8]{6}+6 = 6\\ \sqrt[8]{6}×6÷\sqrt[8]{6} = 6\\ \sqrt[8]{6}÷\sqrt[8]{6}×6 = 6\\ \sqrt[9]{6}+6-\sqrt[9]{6} = 6\\ \sqrt[9]{6}-\sqrt[9]{6}+6 = 6\\ \sqrt[9]{6}×6÷\sqrt[9]{6} = 6\\ \sqrt[9]{6}÷\sqrt[9]{6}×6 = 6\\ 7-7÷7 = 6\\ 7-\sqrt{7}÷\sqrt{7} = 6\\ 7-\sqrt[3]{7}÷\sqrt[3]{7} = 6\\ 7-\sqrt[4]{7}÷\sqrt[4]{7} = 6\\ 7-\sqrt[5]{7}÷\sqrt[5]{7} = 6\\ 7-\sqrt[6]{7}÷\sqrt[6]{7} = 6\\ 7-\sqrt[7]{7}÷\sqrt[7]{7} = 6\\ 7-\sqrt[8]{7}÷\sqrt[8]{7} = 6\\ 7-\sqrt[9]{7}÷\sqrt[9]{7} = 6\\ 8-\sqrt{8}÷\sqrt[6]{8} = 6\\ 8-\sqrt[6]{8}×\sqrt[6]{8} = 6\\ 8÷\sqrt[3]{8}+\sqrt[3]{8} = 6\\ \sqrt{8}×\sqrt[6]{8}+\sqrt[3]{8} = 6\\ \sqrt[3]{8}+8÷\sqrt[3]{8} = 6\\ \sqrt[3]{8}+\sqrt{8}×\sqrt[6]{8} = 6\\ \sqrt[3]{8}+\sqrt[3]{8}+\sqrt[3]{8} = 6\\ \sqrt[3]{8}+\sqrt[3]{8}×\sqrt[3]{8} = 6\\ \sqrt[3]{8}+\sqrt[6]{8}×\sqrt{8} = 6\\ \sqrt[3]{8}×\sqrt[3]{8}+\sqrt[3]{8} = 6\\ \sqrt[6]{8}×\sqrt{8}+\sqrt[3]{8} = 6\\ 9-9÷\sqrt{9} = 6\\ 9-\sqrt[3]{9}×\sqrt[6]{9} = 6\\ 9-\sqrt[4]{9}×\sqrt[4]{9} = 6\\ 9-\sqrt[6]{9}×\sqrt[3]{9} = 6\\ 9÷\sqrt{9}+\sqrt{9} = 6\\ \sqrt{9}+9÷\sqrt{9} = 6\\ \sqrt{9}+\sqrt[3]{9}×\sqrt[6]{9} = 6\\ \sqrt{9}+\sqrt[4]{9}×\sqrt[4]{9} = 6\\ \sqrt{9}+\sqrt[6]{9}×\sqrt[3]{9} = 6\\ \sqrt{9}×\sqrt{9}-\sqrt{9} = 6\\ \sqrt[3]{9}×\sqrt[6]{9}+\sqrt{9} = 6\\ \sqrt[4]{9}×\sqrt[4]{9}+\sqrt{9} = 6\\ \sqrt[6]{9}×\sqrt[3]{9}+\sqrt{9} = 6$$