It’s time to do the math
Python (imperfect) 493 474 - 300 = 174
There are a fair number of issues with this solution, firstly  that it ignores any exponent that is too large (any in which the exponent is greater than 100). I actually don't think this removes any possibilities for inputs less than or equal to 5, but I'm not 100% sure.
Another thing is that it does not consider any unary square roots, as it would get complicated (any solution with any term equal to 0 or 1 would produce an infinite number of solutions). It also does not consider any unary negation (the '-' symbol) for the same reason, as well as the fact that I'm not actually sure if the question asked for it.
I also considered what criteria should decide if two expressions were equivalent, but I couldn't find a way to rigorously define it in a way I found to be intuitive, so (for now at least) I didn't implement anything like that. This does mean that it outputs quite a few results, and it also uses parenthesis in a fairly naive way.
On a side note I think that this might include the longest single line of code I've written, especially before it was fully golfed.
R=range
F=lambda s:lambda a,b:eval(s)
L=lambda D,N:[(int(str(D)*N),str(D)*N)]+[(o(u,v),&quot;(%s%s%s)&quot;%(s,c,t))for p in R(1,N)for u,s in L(D,p)for v,t in L(D,N-p)for c,o in[('+',F('a+b')),('-',F('a-b')),('*',F('a*b')),('/',F(&quot;1.*a/b if b else''&quot;)),('^',F(&quot;''if(a&lt;0 and int(b)!=b)|(a and b&lt;0)|(b&gt;99)else a**b&quot;)),('v',F(&quot;b**(1./a)if a and(a&gt;=0 or b)and(b&gt;=0 or int(1./a)==1./a)&amp;(1./a&lt;99)else''&quot;))]if o(u,v)!='']
A=L(*input())
for i in R(11):
 for v,s in A:
    if v==i:print i,s[1:-1]

Example: ('v' represents '√')
2,3

0 2*(2-2)
0 2v(2-2)
0 (2-2)*2
0 (2-2)/2
0 (2-2)^2
1 2^(2-2)
1 2-(2/2)
1 2v(2/2)
1 (2/2)^2
2 2v(2+2)
2 2+(2-2)
2 2-(2-2)
2 2v(2*2)
2 2*(2/2)
2 2/(2/2)
2 2^(2/2)
2 2v(2^2)
2 (2+2)-2
2 (2+2)/2
2 (2-2)+2
2 (2*2)-2
2 (2*2)/2
2 (2/2)*2
2 (2/2)v2
2 (2^2)-2
2 (2^2)/2
3 2+(2/2)
3 (2/2)+2
6 2+(2+2)
6 2+(2*2)
6 2+(2^2)
6 (2+2)+2
6 (2*2)+2
6 (2^2)+2
8 2*(2+2)
8 2*(2*2)
8 2*(2^2)
8 (2+2)*2
8 (2*2)*2
8 (2^2)*2