diff --git a/petab/v1/math/printer.py b/petab/v1/math/printer.py
index a421989c..d1f7103e 100644
--- a/petab/v1/math/printer.py
+++ b/petab/v1/math/printer.py
@@ -41,7 +41,10 @@ def _print_Pow(self, expr: sp.Pow):
         str_exp = self._print(exp)
         if not base.is_Atom:
             str_base = f"({str_base})"
-        if not exp.is_Atom:
+        # A non-integer Rational exponent (e.g. sqrt -> 1/2) is an Atom but prints as the
+        # multi-token "1/2", so without parentheses "x ^ 1/2" re-parses as (x^1)/2. The
+        # `not exp.is_Atom` check above (#421) misses it; parenthesize it explicitly.
+        if not exp.is_Atom or (exp.is_Rational and not exp.is_Integer):
             str_exp = f"({str_exp})"
         return f"{str_base} ^ {str_exp}"
 
diff --git a/tests/v1/math/test_math.py b/tests/v1/math/test_math.py
index 60bb04b5..3c476c6e 100644
--- a/tests/v1/math/test_math.py
+++ b/tests/v1/math/test_math.py
@@ -43,6 +43,10 @@ def test_printer():
     assert petab_math_str(BooleanTrue()) == "true"
     assert petab_math_str(BooleanFalse()) == "false"
     assert petab_math_str((a + b) ** (c + d)) == "(a + b) ^ (c + d)"
+    # A non-integer rational exponent must be parenthesized, else "a ^ 1/2" re-parses as
+    # (a^1)/2 (i.e. sqrt(a) would round-trip to a/2). See #421 for the base/exponent case.
+    assert petab_math_str(sp.sqrt(a)) == "a ^ (1/2)"
+    assert petab_math_str(a ** sp.Rational(2, 3)) == "a ^ (2/3)"
 
 
 def read_cases():