diff --git a/src/flint/test/test.py b/src/flint/test/test.py
index c19a96d0..67263ca8 100644
--- a/src/flint/test/test.py
+++ b/src/flint/test/test.py
@@ -1279,6 +1279,7 @@ def test_nmod():
     assert G(1,2) != G(0,2)
     assert G(0,2) != G(0,3)
     assert G(3,5) == G(8,5)
+    assert isinstance(hash(G(3, 5)), int)
     assert raises(lambda: G([], 3), TypeError)
     #assert G(3,5) == 8        # do we want this?
     #assert 8 == G(3,5)
@@ -1300,9 +1301,14 @@ def test_nmod():
     assert G(3,17) / G(2,17) == G(10,17)
     assert G(3,17) / 2 == G(10,17)
     assert 3 / G(2,17) == G(10,17)
+    assert G(0,3) / G(1,3) == G(0,3)
     assert G(3,17) * flint.fmpq(11,5) == G(10,17)
     assert G(3,17) / flint.fmpq(11,5) == G(6,17)
+    assert G(1,3) ** 2 == G(1,3)
+    assert G(2,3) ** flint.fmpz(2) == G(1,3)
     assert G(flint.fmpq(2, 3), 5) == G(4,5)
+    assert raises(lambda: G(2,5) ** G(2,5), TypeError)
+    assert raises(lambda: flint.fmpz(2) ** G(2,5), TypeError)
     assert raises(lambda: G(flint.fmpq(2, 3), 3), ZeroDivisionError)
     assert raises(lambda: G(2,5) / G(0,5), ZeroDivisionError)
     assert raises(lambda: G(2,5) / 0, ZeroDivisionError)
@@ -1314,10 +1320,12 @@ def test_nmod():
     assert raises(lambda: G(2,5) - [], TypeError)
     assert raises(lambda: G(2,5) * [], TypeError)
     assert raises(lambda: G(2,5) / [], TypeError)
+    assert raises(lambda: G(2,5) ** [], TypeError)
     assert raises(lambda: [] + G(2,5), TypeError)
     assert raises(lambda: [] - G(2,5), TypeError)
     assert raises(lambda: [] * G(2,5), TypeError)
     assert raises(lambda: [] / G(2,5), TypeError)
+    assert raises(lambda: [] ** G(2,5), TypeError)
     assert G(3,17).modulus() == 17
     assert str(G(3,5)) == "3"
     assert G(3,5).repr() == "nmod(3, 5)"
diff --git a/src/flint/types/nmod.pyx b/src/flint/types/nmod.pyx
index e5e73eb6..87abfb5b 100644
--- a/src/flint/types/nmod.pyx
+++ b/src/flint/types/nmod.pyx
@@ -6,6 +6,7 @@ from flint.types.fmpz cimport fmpz
 from flint.types.fmpq cimport fmpq
 
 from flint.flintlib.fmpz cimport fmpz_t
+from flint.flintlib.nmod cimport nmod_pow_fmpz, nmod_inv
 from flint.flintlib.nmod_vec cimport *
 from flint.flintlib.fmpz cimport fmpz_fdiv_ui, fmpz_init, fmpz_clear
 from flint.flintlib.fmpz cimport fmpz_set_ui, fmpz_get_ui
@@ -89,6 +90,9 @@ cdef class nmod(flint_scalar):
                 return not res
         return NotImplemented
 
+    def __hash__(self):
+        return hash((int(self.val), self.modulus))
+
     def __nonzero__(self):
         return self.val != 0
 
@@ -178,6 +182,8 @@ cdef class nmod(flint_scalar):
                 return NotImplemented
         if tval == 0:
             raise ZeroDivisionError("%s is not invertible mod %s" % (tval, mod.n))
+        if not s:
+            return s
         # XXX: check invertibility?
         x = nmod_div(sval, tval, mod)
         if x == 0:
@@ -195,3 +201,17 @@ cdef class nmod(flint_scalar):
 
     def __invert__(self):
         return (1 / self)   # XXX: speed up
+
+    def __pow__(self, exp):
+        cdef nmod r
+        e = any_as_fmpz(exp)
+        if e is NotImplemented:
+            return NotImplemented
+        r = nmod.__new__(nmod)
+        r.mod = self.mod
+        r.val = self.val
+        if e < 0:
+            r.val = nmod_inv(r.val, self.mod)
+            e = -e
+        r.val = nmod_pow_fmpz(r.val, (<fmpz>e).val, self.mod)
+        return r