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exponentiation Exponentiation is a mathematics, mathematical operation (mathematics), operation, written as , involving two numbers, the ''Base (exponentiation), base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". W ...
, the base is the number b in an expression of the form bn.


Related terms

The number n is called the
exponent Exponentiation is a mathematics, mathematical operation (mathematics), operation, written as , involving two numbers, the ''Base (exponentiation), base'' and the ''exponent'' or ''power'' , and pronounced as " (raised) to the (power of) ". W ...
and the expression is known formally as exponentiation of b by n or the exponential of n with base b. It is more commonly expressed as "the nth power of b", "b to the nth power" or "b to the power n". For example, the fourth power of 10 is 10,000 because . The term ''power'' strictly refers to the entire expression, but is sometimes used to refer to the exponent.
Radix In a positional numeral system, the radix or base is the number of unique numerical digit, digits, including the digit zero, used to represent numbers. For example, for the decimal/denary system (the most common system in use today) the radix (b ...
is the traditional term for ''base'', but usually refers then to one of the common bases: decimal (10), binary (2), hexadecimal (16), or sexagesimal (60). When the concepts of variable and constant came to be distinguished, the process of exponentiation was seen to transcend the algebraic functions. In his 1748 ''Introductio in analysin infinitorum'',
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
referred to "base a = 10" in an example. He referred to ''a'' as a "constant number" in an extensive consideration of the function F(''z'') = ''a''z. First ''z'' is a positive integer, then negative, then a fraction, or rational number.
Leonhard Euler Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ma ...
(1748
Chapter 6: Concerning Exponential and Logarithmic Quantities
of Introduction to the Analysis of the Infinite, translated by Ian Bruce (2013), lk from 17centurymaths.


Roots

When the nth power of b equals a number a, or a = bn, then b is called an " nth root" of a. For example, 10 is a fourth root of 10,000.


Logarithms

The
inverse function In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in ...
to exponentiation with base b (when it is well-defined) is called the
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 of ...
to base b, denoted logb. Thus: :log''b'' ''a'' = ''n''. For example, log10 10,000 = 4.


References

{{Reflist Exponentials Mathematical terminology