diff --git a/src/rulesets/Base/fastmath_able.jl b/src/rulesets/Base/fastmath_able.jl
index d8afb630a..18ee18151 100644
--- a/src/rulesets/Base/fastmath_able.jl
+++ b/src/rulesets/Base/fastmath_able.jl
@@ -181,8 +181,14 @@ let
         ## power
         # literal_pow is in base.jl
         function frule((_, Δx, Δp), ::typeof(^), x::Number, p::Number)
-            y = x ^ p
-            _dx = _pow_grad_x(x, p, float(y))
+            if isinteger(p)
+                tmp = x ^ (p - 1)
+                y = x * tmp
+                _dx = p * tmp
+            else
+                y = x ^ p
+                _dx = _pow_grad_x(x, p, float(y))
+            end
             if iszero(Δp)
                 # Treat this as a strong zero, to avoid NaN, and save the cost of log
                 return y, _dx * Δx