Powers
======

Save both functions into the file  ``powers.py``.

1. Write the function :py:func:`powers_1` that takes two positive
   integers, ``x`` and ``maxn``, and returns the average of the
   sequence of powers of ``x`` less than or equal to ``maxn``. Examples:
   
      .. literalinclude:: powers-1.txt
         :language: python3
         :lines: 3-

   .. note::
        More tests are provided in file :download:`powers-1.txt <powers-1.txt>`

2. Write the function :py:func:`powers_2` that takes two positive
   integers, ``x`` and ``maxn``, and another integer, ``d``, such that
   ``0<=d<10``, and returns the first number of the sequence of powers
   of ``x`` less than or equal to ``maxn`` such that its digit in the
   units position is ``d``. If there is no such number, this function
   must return ``-1``. Examples:
   
      .. literalinclude:: powers-2.txt
         :language: python3
         :lines: 3-

   .. note::
         More tests are provided in file :download:`powers-2.txt <powers-2.txt>`


.. rubric:: Solution

A solution is provided in file :download:`powers.py <solutions/powers.py>`