Exponents and Powers
An exponent tells us how many times a number is multiplied by itself. The number being multiplied is called the base, and the small raised number is called the exponent. The whole expression is called a power.
For example, in $2^4$, the number 2 is the base and the number 4 is the exponent. The expression $2^4$ is a power and is read as “two to the fourth power”.
The exponent 4 tells us to use the base 2 as a factor four times. So we can say that two to the fourth power is sixteen.
Here, the exponent 3 tells us to multiply 3 by itself three times. We read $3^3$ as “three to the third power”. We can also say “three cubed”.
The exponent 2 also has a special name. For example, $5^2$ can be read as “five to the second power” or “five squared”.
Special exponents
There are several important exponent rules that we need to remember.
Any non-zero number raised to the exponent 0 equals 1:
For example:
A number raised to the exponent 1 stays the same:
For example:
Negative exponents
A negative exponent means that we take the reciprocal of the corresponding positive power.
For example:
This rule applies when the base is not zero.
Fractional exponents
A fractional exponent represents a root. An exponent of $1/n$ means the n-th root of the number.
For example, an exponent of $1/2$ means a square root:
An exponent of $1/3$ means a cube root:
