text: When an exponent is a positive integer, that exponent indicates how many copies of the base are multiplied together. For example, . The base  appears  times in the multiplication, because the exponent is . Here,  is the 5th power of 3, or 3 raised to the 5th power.
  The word "raised" is usually omitted, and sometimes "power" as well, so  can be simply read "3 to the 5th", or "3 to the 5". Therefore, the exponentiation  can be expressed as "b to the power of n", "b to the nth power", "b to the nth", or most briefly as "b to the n".
  Integer exponents
  The exponentiation operation with integer exponents may be defined directly from elementary arithmetic operations.
  Positive exponents
  The definition of the exponentiation as an iterated multiplication can be formalized by using induction, and this definition can be used as soon one has an associative multiplication:
  The base case is
  and the recurrence is
  The associativity of multiplication implies that for any positive integers  and ,
  and
  Zero exponent
  As mentioned earlier, a (nonzero) number raised to the  power is :
  This value is also obtained by the empty product convention, which may be used in every algebraic structure with a multiplication that has an identity. This way the formula