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)