Make Three from One

Question

Given a single digit integer and a three digit integer, output a mathematical formula that uses only the single digit and a given list of operators to equal the three digit integer.

Input: A one digit positive integer (1-9) and a three digit integer (100-999)

Output: A mathematical formula meeting the following requirements:

• The only number used is the one digit integer
• There no more than 15 instances of that integer (Prevents trivial solutions of the format (a+a+...+a+a)/a=n)
• The mathematical solution of the formula is the three digit integer
• The only operations allowed are as follows:
  • Addition: 1+1
  • Subtraction: 2-2
  • Multiplication: 3×3, 3*3, (3)3
  • Division: 4÷4, 4/4
  • Exponentiation: 5⁵, 5^5, 5**5
  • Concatenation: 66, 6||6
  • Brackets: (7+7)

Clarifications:

• Input and Output can be in any standard format.
• The symbols for each operation do not need to be what is shown above; they can be whatever makes sense for your language.
• Explain any input or output formats that you think may not be immediately understood.
• Standard loopholes are forbidden.
• If your output doesn't follow the standard order of operations, it shouldn't matter but do make a note. It would help to include brackets as needed to make the order clear.
• You can not concatenate calculated values: (8+8)8 is 128, not 168. However, 88+88−8=168 is valid.
• You may assume the input will always be valid.
• You may assume a valid output will always be possible.
• It does not have to be the shortest possible formula so long as it's valid and uses <16 instances of the single digit

Examples:

Input         Output
[1,123]       11^(1+1)+1+1
999,2         (2+2/2)2×222/2
3 729         3^(3+3)          
['4','300']   ['|','+','**']   where there is a 4 before and after each element and | is concatenate. (4|4+4**4 = 44+4**4 = 44+256 = 300)
255 5         ((5×(5×(5+5)))+5)
6 333         6*666/(6+6)
7,952         7×(7+((7+7)/7)7)+7 
8|517         8 × 8 × 8 + 8 − ( 8 + 8 + 8 ) / 8
999 9         999

Scoring

This is code-golf so the shortest code wins.