diff --git a/tests/compiler/ir/test_optimize_ir.py b/tests/compiler/ir/test_optimize_ir.py
index 80eab3cbdd9..86405b76112 100644
--- a/tests/compiler/ir/test_optimize_ir.py
+++ b/tests/compiler/ir/test_optimize_ir.py
@@ -74,6 +74,13 @@
     (["mod", "x", 128], ["and", "x", 127]),
     (["sdiv", "x", 64], ["sdiv", "x", 64]),  # no-op
     (["smod", "x", 64], ["smod", "x", 64]),  # no-op
+    (["exp", 3, 5], [3**5]),
+    (["exp", 3, 256], [(3**256) % (2**256)]),
+    (["exp", 2, 257], [0]),
+    (["exp", "x", 0], ["iszero", "x"]),
+    (["exp", "x", 1], ["x"]),
+    (["exp", 1, "x"], [1]),
+    (["exp", 0, "x"], [0]),
     # bitwise ops
     (["shr", 0, "x"], ["x"]),
     (["sar", 0, "x"], ["x"]),
diff --git a/vyper/ir/optimizer.py b/vyper/ir/optimizer.py
index 0fec39b6e0f..69ef6b5684a 100644
--- a/vyper/ir/optimizer.py
+++ b/vyper/ir/optimizer.py
@@ -47,6 +47,7 @@ def _is_int(node: IRnode) -> bool:
     "sdiv": (evm_div, "/", SIGNED),
     "mod": (evm_mod, "%", UNSIGNED),
     "smod": (evm_mod, "%", SIGNED),
+    "exp": (operator.pow, "**", UNSIGNED),
     "eq": (operator.eq, "==", UNSIGNED),
     "ne": (operator.ne, "!=", UNSIGNED),
     "lt": (operator.lt, "<", UNSIGNED),
@@ -165,6 +166,20 @@ def _conservative_eq(x, y):
         new_val = "sub"
         new_args = [0, args[0]]
 
+    elif binop == "exp":
+        # n ** 0 == (0 if n == 0 else 1)
+        if _int(args[1]) == 0:
+            new_val = "iszero"
+            new_args = [args[0]]
+        # n ** 1 == n
+        if _int(args[1]) == 1:
+            new_val = args[0].value
+            new_args = args[0].args
+        # 0 ** n == 0; 1 ** n == 1
+        if _int(args[0]) in (0, 1):
+            new_val = _int(args[0])
+            new_args = []
+
     # maybe OK:
     # elif binop == "div" and _int(args[1], UNSIGNED) == MAX_UINT256:
     #    # (div x (2**256 - 1)) == (eq x (2**256 - 1))