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A group (or subgroup) that consists of all powers of a specific element x is the cyclic group generated by x. If all the powers of x are distinct, the group is isomorphic to the additive group Z {\displaystyle \mathbb {Z} } of the integers.
Exponents. The exponent of a number says how many times to use the number in a multiplication. In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".
Laws of Exponents. Exponents are also called Powers or Indices. The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". Try it yourself:
Basic rules for exponentiation. If n is a positive integer and x is any real number, then xn corresponds to repeated multiplication. xn = x × x × ⋯ × x n times. We can call this “ x raised to the power of n,” “ x to the power of n,” or simply “ x to the n.” Here, x is the base and n is the exponent or the power.
The power, index, or exponent of a value (called the base) is a number indicating how many times that value multiplies by itself. We write the power of a value slightly above it to the right or using the hat (^) symbol. For example, 5 x 5 = 5 2 = 5^2.
Definition of Exponent. The exponent of a number indicates the total time to use that number in a multiplication. For example, 8 × 8 × 8 can be expressed as 8 3 because 8 is multiplied by itself 3 times.
A power is an exponent to which a given quantity is raised. The expression is therefore known as " to the th power." A number of powers of are plotted above (cf. Derbyshire 2004, pp. 68 and 73). The power may be an integer, real number, or complex number.
