diff --git a/src/expression_parser/shunting_yard.rs b/src/expression_parser/shunting_yard.rs
index 16bb5b7..bb3d476 100644
--- a/src/expression_parser/shunting_yard.rs
+++ b/src/expression_parser/shunting_yard.rs
@@ -11,11 +11,13 @@
  * expression parser.
  */
 
+#[derive(PartialEq)]
 enum Associativity {
     Right,
     Left
 }
 
+#[derive(PartialEq)]
 pub struct Operator {
     character: char,
     precedence: u8,
@@ -29,6 +31,17 @@ impl Operator {
         }
         return false;
     }
+
+    pub fn get_operator(c: char) -> Option<Operator> {
+        match c {
+            '+' => Some(ADDITION),
+            '-' => Some(SUBTRACTION),
+            '*' => Some(MULTIPLICATION),
+            '/' => Some(DIVISION),
+            '^' => Some(EXPONENTIATION),
+            _ => None
+        }
+    }
 }
 
 const ADDITION: Operator = Operator {
@@ -58,7 +71,7 @@ const DIVISION: Operator = Operator {
 const EXPONENTIATION: Operator = Operator {
     character: '*',
     precedence: 2,
-    associativity: Associativity::Left
+    associativity: Associativity::Right
 };
 
 const OPERATORS: [Operator; 5] = [ADDITION, SUBTRACTION, MULTIPLICATION, DIVISION, EXPONENTIATION];
@@ -68,38 +81,78 @@ pub fn form_reverse_polish_notation(regular_math: &str) -> Result<String, String
     let mut input_queue: Vec<char> = regular_math.chars().rev().collect();
     let mut operator_stack: Vec<char> = Vec::new();
 
-    // process all tokens first.
+    // while there are tokens to br read:
     while !(input_queue.is_empty()) {
-        let token: char = *(input_queue.last().unwrap());
-        input_queue.pop();
+        // read a token
+        let token: char = input_queue.pop().unwrap();
         dbg!(&token);
             
+        // if the token is:
+        // a number:
         if token.is_numeric() {
-            println!("number");
-        }
-        else if Operator::is_operator(token) {
-            println!("operator");
-        }
-        // Unnessecary, will be processed by the expression parser
-        //else if '(' == token {
-        //    println!("(");
-        //}
-        //else if ')' == token {
-        //    println!(")");
-        //}
-        else {
-            eprintln!("Unrecognized token:  '{token}'");
-            std::process::exit(1);
+            // put it into the output_queue
+            output_queue.push(token);
         }
+        // a function
+        // handled by the expression parser
 
+        // a operator o1
+        else if Operator::is_operator(token) {
+            // (get the constant Operator (which is a struct) that fits to that token.)
+            let o1 = match Operator::get_operator(token) {
+                Some(valid_op) => valid_op,
+                None => {panic!("Operator '{token}' not found.");},
+            };
+            
+            // while there is an operator o2 at the top of the stack 
+            if !operator_stack.is_empty() {
+                dbg!(&operator_stack);
+                dbg!(&operator_stack);
+                let o2 = match Operator::get_operator(*(operator_stack.clone().last().clone().unwrap())) {
+                    Some(valid_op) => valid_op,
+                    None => {panic!("Operator '{token}' not found.");},
+                };
+                // and
+                // (o2 has greater precedence than o1 or (o1 and o2 have the same precedence and o1
+                // is left associative))
+                while ((operator_stack.last().is_some()) & ((o2.precedence > o1.precedence) | ((o1.precedence == o2.precedence) & (o1.associativity == Associativity::Left)))) {
+                    dbg!(&operator_stack);
+                    println!("REACHED THE MAGIC WHILE");
+                    // pop o2 from the operator stack into the output queue.
+                    // after this debug statement, the operator_stack is empty for no reason!!!!
+                    // FIXME
+                    let my_c = match operator_stack.pop() {
+                        Some(c) => c,
+                        None => {panic!("weirdly gone!")},
+                        };
+                    output_queue.push(my_c);
+                }
+            }
+            operator_stack.push(o1.character);
+        }
+        /*
+        // Unnessecary, will be processed by the expression parser
+        else if '(' == token {
+            println!("(");
+        }
+        else if ')' == token {
+            println!(")");
+        }
+        */
+        else {
+            return Err("Unrecognized token: '{token}'".to_string());
+        }
     }
+    dbg!(&output_queue);
 
     // afterwards, process any operators still on the operator_stack
     while !(operator_stack.is_empty()) {
-        todo!();
+        output_queue.push(operator_stack.pop().unwrap());
     }
 
-    Ok("TODO".to_string())
+    dbg!(&output_queue);
+    let rpn: String = output_queue.iter().cloned().collect::<String>();
+    Ok(rpn)
 }
 
 // after we have the rpn, we may want to calculate the values with it.