power,” or “three with an exponent of four.”) (For more information on exponents, see
“Math Basics.”) The exponent represents the number of times a number is being mul-
tiplied. The above example, for instance, actually means “3 3 3 3,” which is
equal to 81. The power can be an integer (negative or positive numbers), real number,
or even a complex number. This can also be thought of as taking the quantity b,the
base number, to the power of another quantity often called e,the exponent. (In many
computer-oriented texts, this is written as b^ e.)
Exponents are important to algebra as they are often included in algebraic equa-
tions. The process of performing the operation of raising to a power is known as expo-
nentiation. Exponents are also often associated with functions. For example, in the
function f(x) x^2 , the 2 is the exponent.
What is a basein algebra?
The base is used in algebra in connection with powers. In fact, it is called the base of a
power—or the number that is used as a factor a given number of times. In the exam-
ple 3^4 , 3 is the base. The base can either be the number used with an exponent to cre-
ate a power, such as the 3 in 3^4 , or a number written as a subscript, such as with a log-
arithm (for example, logax,in which ais the base number). (See below for more
information about logarithms; for more information about bases, see “Math Basics.”)
What are some simple rulesof exponents?
There are several simple rules when it comes to exponents. These include the following:
- The equation x^1 x(or a number raised to the 1 power is the number itself;
this is also called the “rules of 1”).
- The equation x^0 1 (unless x0, which is considered undefined; this is also
called the “zero rule”).
- A number without an exponent has an exponent of 1, as in 20 201.
- A negative exponent indicates that the number is to be divided by the exponent
instead of multiplied. For example, 3^3 is equal to 1/(3^3 ), or 1/27. But there is a
restriction to this rule: xn1/xnonly when xis not zero; if xis 0, then xnis
undefined.
What are some rulesfor combining exponents?
There are also rules for combining exponents (called the laws of indices):
- To multiply exponents with identical bases, add the exponents, such as 3^2 33
35 (3 is the base).
- To multiply like exponents, combine terms, such as 10^2 22 (10 2)^2 400.
- To divide identical bases, subtract the exponents, such as 10^3 /10 103 ^1 102
144 100 (the denominator 10 has an assumed exponent of 1).
