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diff --git a/testsuite/tests/lib/base/T19569.hs b/testsuite/tests/lib/base/T19569.hs
new file mode 100644
index 0000000000..00f7c7367b
--- /dev/null
+++ b/testsuite/tests/lib/base/T19569.hs
@@ -0,0 +1,56 @@
+-- This program is meant to compare the bracketing produced by the
+-- actual implementation of (^) with the bracketing in the RHS of its
+-- rewrite rules for known small powers, and complains if they disagree.
+
+{-# OPTIONS_GHC -O -Wno-missing-methods #-}
+
+module Main where
+
+import Control.Monad
+import Data.Typeable
+import Numeric.Natural
+import Text.Printf
+
+data MulTree = X | FromInteger Integer | Mul MulTree MulTree
+  deriving (Eq, Show)
+
+instance Num MulTree where
+  fromInteger = FromInteger
+  (*) = Mul
+
+opaquePow :: (Num a, Integral b) => a -> b -> a
+{-# NOINLINE opaquePow #-}
+opaquePow k e = k ^ e
+
+checkRules
+  :: forall expTy. (Integral expTy, Show expTy, Typeable expTy)
+  => expTy -> IO ()
+{-# INLINE checkRules #-}
+checkRules _ = let
+  checkOne :: expTy -> IO ()
+  {-# INLINE checkOne #-}
+  checkOne e = when (X ^ e /= opaquePow X e) (reportProblem (X ^ e) e)
+  reportProblem :: MulTree -> expTy -> IO ()
+  reportProblem wrongVal e = do
+    printf "Problem with exponent (%s :: %s)\n" (show e) (show $ typeOf e)
+    printf "  Expected: %s\n" (show $ opaquePow X e)
+    printf "  Actual:   %s\n" (show wrongVal)
+  in  do
+  checkOne 0
+  checkOne 1
+  checkOne 2
+  checkOne 3
+  checkOne 4
+  checkOne 5
+  checkOne 6
+  checkOne 7
+  checkOne 8
+  checkOne 9
+  checkOne 10
+
+main :: IO ()
+main = do
+  checkRules (0 :: Integer)
+  checkRules (0 :: Natural)
+  checkRules (0 :: Int)
+  checkRules (0 :: Word)