diff --git a/src/Math/Haskellator/Internal/AstProcessingSteps/Evaluate.hs b/src/Math/Haskellator/Internal/AstProcessingSteps/Evaluate.hs
index 9820c71..c904089 100644
--- a/src/Math/Haskellator/Internal/AstProcessingSteps/Evaluate.hs
+++ b/src/Math/Haskellator/Internal/AstProcessingSteps/Evaluate.hs
@@ -28,7 +28,7 @@ execute :: Expr                           -- ^ the expression tree to evaluate
         -> Either Error (Value Dimension) -- ^ the result or an error
 execute expr = do
     r <- runAstFold $ execute' expr
-    return $ r { unit = filterUnwanted $ unit r }
+    return $ r { unit = filterZeroPower $ unit r }
 
 execute' :: Expr -> SimpleAstFold (Value Dimension)
 execute' = partiallyFoldExprM execVal execBinOp execUnaryOp execConversion execVarBinds execVar
@@ -48,10 +48,10 @@ execBinOp lhs Div   rhs = do
     let u = subtractUnits (unit lhs) (unit rhs)
     return $ Value (value lhs / value rhs) u
 execBinOp lhs Pow   rhs = case rhs of
-    Value _ [UnitExp Multiplier _] -> return $ Value (value lhs ** value rhs) ((\u -> u {
+    Value _ [] -> return $ Value (value lhs ** value rhs) ((\u -> u {
         power = power u * (round (value rhs) :: Int)
       }) <$> unit lhs)
-    _                              -> throwError $ Error RuntimeError "Exponentiation of units is not supported"
+    _          -> throwError $ Error RuntimeError "Exponentiation of units is not supported"
 execBinOp _   op    _   = throwError $ Error ImplementationError $ "Unknown binary operator " ++ show op
 
 execUnaryOp :: Op -> Value Dimension -> SimpleAstFold (Value Dimension)
@@ -105,11 +105,5 @@ findPair x (y:ys) | dimUnit x == dimUnit y = ([(x, y)], ([], ys))
                   | otherwise              = let (pair, (lr, rr)) = findPair x ys
                                               in (pair, (lr, y:rr))
 
-filterUnwanted :: Dimension -> Dimension
-filterUnwanted = filterZeroPower . filterMultiplier
-
 filterZeroPower :: Dimension -> Dimension
 filterZeroPower = filter ((/=0) . power)
-
-filterMultiplier :: Dimension -> Dimension
-filterMultiplier = filter (not . isMultiplier . dimUnit)
diff --git a/src/Math/Haskellator/Internal/AstProcessingSteps/Normalize.hs b/src/Math/Haskellator/Internal/AstProcessingSteps/Normalize.hs
index 913e6bc..447401a 100644
--- a/src/Math/Haskellator/Internal/AstProcessingSteps/Normalize.hs
+++ b/src/Math/Haskellator/Internal/AstProcessingSteps/Normalize.hs
@@ -17,7 +17,7 @@ import Math.Haskellator.Internal.Utils.Error
 -- | Normalize all values inside the tree to their base units
 normalize :: Expr              -- ^ the 'Expr' tree to normalize
           -> Either Error Expr -- ^ the normalized 'Expr' tree
-normalize = Right . foldExpr (Val . convertDimensionToBase) BinOp UnaryOp Conversion VarBindings Var
+normalize = Right . foldExpr (Val . filterMultiplier . convertDimensionToBase) BinOp UnaryOp Conversion VarBindings Var
 
 -- | Converts a value to its base dimension
 -- >>> convertDimensionToBase $ Value 1 [UnitExp Kilometer 2, UnitExp Hour 1]
@@ -59,3 +59,6 @@ convertUnit s (t:ts) val@(Value v u) = case convertTo (Value 1 s) t of
     Nothing            -> do
         (v', rest) <- convertUnit s ts val
         return (v', t:rest)
+
+filterMultiplier :: AstValue -> AstValue
+filterMultiplier (Value v u) = Value v $ filter (not . isMultiplier . dimUnit) u
diff --git a/src/Math/Haskellator/Internal/Parser.hs b/src/Math/Haskellator/Internal/Parser.hs
index 046ffeb..a252625 100644
--- a/src/Math/Haskellator/Internal/Parser.hs
+++ b/src/Math/Haskellator/Internal/Parser.hs
@@ -35,6 +35,7 @@ import Control.Monad.State
 import Data.Bifunctor
 
 import Math.Haskellator.Internal.AstProcessingSteps.Evaluate
+import Math.Haskellator.Internal.AstProcessingSteps.Normalize
 import Math.Haskellator.Internal.DerivedUnits
 import Math.Haskellator.Internal.Expr
 import Math.Haskellator.Internal.Lexer
@@ -164,7 +165,7 @@ parseUnitExp = do
     either (\x -> fail $ "Invalid unit " ++ x) (\dim -> do {
         requireOperator "^";
         expr <- parsePrimary;
-        case execute expr of
+        case normalize expr >>= execute of
             Right (Value v []) -> let e = round v :: Int in return ((\(UnitExp u e') -> UnitExp u $ e' * e) <$> dim)
             _                  -> fail "Exponentiation of units is not supported"
     } <|> return dim) $ parseUnitSymbol i
diff --git a/test/Evaluation.hs b/test/Evaluation.hs
index 30c24b8..2c31f17 100644
--- a/test/Evaluation.hs
+++ b/test/Evaluation.hs
@@ -40,8 +40,8 @@ normalization = testGroup "Normalization" [
       @?= Right (BinOp (Val $ Value 1 $ meter 42) Div (Val $ Value 1 $ second 33))
   ]
 
-evalString :: String -> Either Error Double
-evalString = scan >=> parse >=> evaluate
-
 normalizeString :: String -> Either Error Expr
 normalizeString = scan >=> parse >=> normalize
+
+evalString :: String -> Either Error Double
+evalString = normalizeString >=> evaluate
diff --git a/test/Parser.hs b/test/Parser.hs
index ae56998..70ab52c 100644
--- a/test/Parser.hs
+++ b/test/Parser.hs
@@ -65,7 +65,7 @@ genInt = do
 instance Arbitrary Unit where
     -- Multiplier needs to be excluded here to prevent ambiguous cases in our grammar
     -- e.g. 2^2 could be either a multiplier with exponent two or a power operation on two multipliers with exponent 1
-    arbitrary = arbitraryBoundedEnum `suchThat` (/= Multiplier)
+    arbitrary = arbitraryBoundedEnum `suchThat` (not . isMultiplier)
 
 instance Arbitrary Expr where
   arbitrary = let randomValue = do {