1981:
1: 1^981
2: 1^98+1
3: 1+9-8+1
4: -1-sqrt(9)+8*1
5: -1-sqrt(9)+8+1
6: -1*sqrt(9)+8+1
7: 1-sqrt(9)+8+1
8: 1^9*8*1
9: 1^9*8+1
10: 1^9+8+1
11: 19-8*1
12: 19-8+1
13: 1+(sqrt(9))!+(sqrt(8+1))!
14: 1*(sqrt(9))!+(sqrt(8+1))! or 1+(sqrt(9))!+8-1
15: -1+9+8-1
16: -1+9+8*1
17: -1+9+8+1 or 1*9+8*1
18: 1*9+8+1
19: 1+9+8+1
20: -1+(sqrt(9))*(8-1)
21: 1*(sqrt(9))*(8-1)
22: 1+(sqrt(9))*(8-1) or -1+(sqrt(9))*8-1
23: -1+(sqrt(9))*8*1
24: 1*(sqrt(9))*8*1
25: 1+(sqrt(9))*8*1
26: 1+(sqrt(9))*8+1 or 19+8-1
27: 19+8*1
28: 19+8+1
29: 1*sqrt(9)+ [sqrt(((sqrt(8+1))!)!)]
30: (1+3)!+(sqrt(8+1))!
31: (1+sqrt(9))*8-1
32: (1+sqrt(9))*8*1
33: (1+sqrt(9))*8+1
34: -1+[sqrt((sqrt(9))!)!)]+8+1
35: (-1+(sqrt(9)!))*(8-1)
36: 1*(sqrt(9))! * (sqrt(8+1))!
37: 1+(sqrt(9))! * (sqrt(8+1))! or 19*[sqrt(8)]-1
38: 19*[sqrt(8)]*1
39: 19*[sqrt(8)]+1 or (-1+(sqrt(9))!)*8-1
40: (-1+(sqrt(9))!)*8*1
41: (-1+(sqrt(9))!)*8+1 or -1+(sqrt(9))!*(8-1)
42: 1*(sqrt(9))!*(8-1)
43: 1+(sqrt(9))!*(8-1)
44: [sqrt(1981)]
45: (-1+(sqrt(9))!)*(8+1)
46: -1+(sqrt(9))!*8-1
47: -1+(sqrt(9))!*8*1
48: 1*(sqrt(9))!*8*1
49: 1+(sqrt(9))!*8*1
50: 1+(sqrt(9))!*8+1
51: -1 + [sqrt((((sqrt(9))!))!)] + [sqrt((((sqrt(8+1))!))!)]
52: 1 * [sqrt((((sqrt(9))!))!)] + [sqrt((((sqrt(8+1))!))!)]
53: 1 + [sqrt((((sqrt(9))!))!)] + [sqrt((((sqrt(8+1))!))!)] or -1+(sqrt(9))! * (8+1)
54: 1*(sqrt(9))! * (8+1)
55: 1+(sqrt(9))! * (8+1)
56: (1+(sqrt(9))!)*8*1
57: (1+(sqrt(9))!)*8+1 or 19*sqrt(8+1)
58: 1-[sqrt([((sqrt(9))!)])]+81
59: (-1+((sqrt(9))!)) / [sqrt(8)] - 1
60: (1+9)*((sqrt(8+1))!)
61: (-1+((sqrt(9))!)) / [sqrt(8)] + 1
62: -19+81
63: (-1+9)*8-1
64: (-1+9)*8*1
65: (-1+9)*8+1
66: 1*[((sqrt(9))!) / (8+1)]
67: 1+[((sqrt(9))!) / (8+1)]
68: 1 - sqrt(9) + [sqrt((8-1)!)]
69: -1^9 + [sqrt((8-1)!)]
70: 1^9 * [sqrt((8-1)!)] or -1+9*8-1
71: -1+9*8*1
72: 1*9*8*1
73: 1+9*8*1 or -18+91
74: 1+9*8+1
75: -1*((sqrt(9))!)+81
76: 1-((sqrt(9))!)+81
77: -1-sqrt(9)+81
78: -1*sqrt(9)+81
79: (1+9)*8-1
80: (1+9)*8*1 or -1^9+81
81: (1+9)*8+1 or 1^9*81 or 1*9*(8+1)