diff --git a/pint/quantity.py b/pint/quantity.py
index 22bcfbf..d9286ba 100644
--- a/pint/quantity.py
+++ b/pint/quantity.py
@@ -893,9 +893,21 @@ class _Quantity(SharedRegistryObject):
 
             if isinstance(getattr(other, '_magnitude', other), ndarray):
                 # arrays are refused as exponent, because they would create
-                #  len(array) quanitites of len(set(array)) different units
-                if np.size(other) > 1:
-                    raise DimensionalityError(self._units, 'dimensionless')
+                # len(array) quantities of len(set(array)) different units
+                # unless the base is dimensionless.
+                if self.dimensionless:
+                    if getattr(other, 'dimensionless', False):
+                        self._magnitude **= other.m_as('')
+                        return self
+                    elif not getattr(other, 'dimensionless', True):
+                        raise DimensionalityError(other._units, 'dimensionless')
+                    else:
+                        self._magnitude **= other
+                        return self
+                elif np.size(other) > 1:
+                    raise DimensionalityError(self._units, 'dimensionless',
+                                              extra_msg='Quantity array exponents are only allowed '
+                                                        'if the base is dimensionless')
 
             if other == 1:
                 return self
@@ -930,9 +942,19 @@ class _Quantity(SharedRegistryObject):
 
             if isinstance(getattr(other, '_magnitude', other), ndarray):
                 # arrays are refused as exponent, because they would create
-                #  len(array) quantities of len(set(array)) different units
-                if np.size(other) > 1:
-                    raise DimensionalityError(self._units, 'dimensionless')
+                # len(array) quantities of len(set(array)) different units
+                # unless the base is dimensionless.
+                if self.dimensionless:
+                    if getattr(other, 'dimensionless', False):
+                        return self.__class__(self.m ** other.m_as(''))
+                    elif not getattr(other, 'dimensionless', True):
+                        raise DimensionalityError(other._units, 'dimensionless')
+                    else:
+                        return self.__class__(self.m ** other)
+                elif np.size(other) > 1:
+                    raise DimensionalityError(self._units, 'dimensionless',
+                                              extra_msg='Quantity array exponents are only allowed '
+                                                        'if the base is dimensionless')
 
             new_self = self
             if other == 1:
diff --git a/pint/testsuite/test_issues.py b/pint/testsuite/test_issues.py
index 4a9e8b7..05a432c 100644
--- a/pint/testsuite/test_issues.py
+++ b/pint/testsuite/test_issues.py
@@ -546,4 +546,11 @@ class TestIssuesNP(QuantityTestCase):
         x = ureg.Quantity(1., 'meter')
         y = f(x)
         z = x * y
-        self.assertEquals(z, ureg.Quantity(1., 'meter * kilogram'))
\ No newline at end of file
+        self.assertEquals(z, ureg.Quantity(1., 'meter * kilogram'))
+
+    def test_issue483(self):
+        ureg = self.ureg
+        a = np.asarray([1, 2, 3])
+        q = [1, 2, 3] * ureg.dimensionless
+        p = (q ** q).m
+        np.testing.assert_array_equal(p, a ** a)
\ No newline at end of file
diff --git a/pint/testsuite/test_numpy.py b/pint/testsuite/test_numpy.py
index ea23c8e..7d3271c 100644
--- a/pint/testsuite/test_numpy.py
+++ b/pint/testsuite/test_numpy.py
@@ -427,7 +427,7 @@ class TestNDArrayQunatityMath(QuantityTestCase):
     @helpers.requires_numpy()
     def test_exponentiation_array_exp(self):
         arr = np.array(range(3), dtype=np.float)
-        q = self.Q_(arr, None)
+        q = self.Q_(arr, 'meter')
 
         for op_ in [op.pow, op.ipow]:
             q_cp = copy.copy(q)