To convert the expression "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3" into Reverse Polish Notation (also known as postfix notation), you can use the shunting-yard algorithm. This algorithm processes operators and operands according to their precedence and associativity. Here's how you can convert the expression:

1. Initialize an empty stack for operators.
2. Initialize an empty list for the output (the reverse Polish notation).
3. Iterate through each token (operands and operators) in the infix expression.
4. If the token is an operand, add it to the output list.
5. If the token is a left parenthesis, push it onto the operator stack.
6. If the token is a right parenthesis, pop operators from the stack and add them to the output list until a matching left parenthesis is encountered. Pop and discard the left parenthesis.
7. If the token is an operator:
   a. While there are operators at the top of the stack with greater precedence or equal precedence and left associativity, pop them from the stack and add them to the output list.
   b. Push the current operator onto the stack.
8. After processing all tokens, pop any remaining operators from the stack and add them to the output list.

Let's apply this algorithm to the given expression:

Infix expression: "3 + 4 * 2 / ( 1 - 5 ) ^ 2 ^ 3"

Output (Reverse Polish Notation): "3 4 2 * 1 5 - 2 3 ^ ^ / +"

Here's the expression step-by-step:

1. Push "3" onto the stack.
2. Push "+" onto the stack.
3. Push "4" onto the stack.
4. Push "*" onto the stack.
5. Push "2" onto the stack.
6. Push "/" onto the stack.
7. Push "(" onto the stack.
8. Push "1" onto the stack.
9. Push "-" onto the stack.
10. Push "5" onto the stack.
11. Pop and add operators "^" (twice) to the output.
12. Pop and discard "(".
13. Pop and add "/" to the output.
14. Pop and add "*" to the output.
15. Pop and add "+" to the output.

So, the reverse Polish notation is "3 4 2 * 1 5 - 2 3 ^ ^ / +".