# exponent

An exponent is a quantity representing the power to which some other quantity is raised. Exponents do not have to be numbers or constants; they can be variables. They are often positive whole number s, but they can be negative number s, fractional number s, irrational number s, or complex number s.

Consider the following mathematical expressions:

*y* = *e ^{x}*

*x*

^{3}+ 5

*x*

^{2}- 5

*x*+ 6 = 0

*x*

^{2}+

*y*

^{2}=

*z*

^{2}

In the first expression, *x* is the exponent of *e* . In the second expression, the numbers 3 and 2 are exponents of *x* . In the third expression, the number 2 is an exponent of *x* , *y* , and *z* .

Exponents are important in scientific notation, when large or small quantities are denoted as powers of 10. Consider this expression of a large number:

534,200,000,000 = 5.342 x 10 ^{11}

Here, the exponent 11, attached to the base 10, indicates the quantity 100,000,000,000.

In conventional documentation, exponents are denoted by superscripts, as in the examples above. But it is not always possible to write them this way. When sending an e-mail message, the body of text must be in plain ASCII , which does not support specialized character attributes such as superscripts. If *x* is the exponent to which some base quantity *a* is raised, then *a ^{x}* can be written in ASCII as a^x. In scientific notation, the uppercase letter E can be used to indicate that a number is raised to a positive or negative power of 10. That power is usually indicated by two-digit numbers between -99 and +99. Here are some examples:

2.45 x 10 ^{6} = 2.45E+06

6.0033 x 10 ^{-17} = 6.0033E-17

Also see logarithm .

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