We want to define the term power using the words base and exponent. We are also asked to provide some examples.

Definiton

A power is a number or expression that represents a product of repeated factors. Its notation is made up of a base — the number being multiplied — and an exponent, which gives the number of times the base appears in the multiplication.

Example

Consider the following example.

5^{4}

Here the base is

5

and the exponent is

4 .

This means that

5

is multiplied by itself

4

times.

5^{4} = 4 5 \cdot 5 \cdot 5 \cdot 5

We see that powers allow us to write repeated multiplications in a shorter way.

Extra

Reading powers

Most exponential expressions are read in the same way, whether they are numeric or algebraic.

Expression	Example $1$	Example $2$
$7^{4}$	$7$ raised to the power of $4$	$7$ raised to the fourth power
$x^{9}$	$x$ to the power of $9$	$x$ to the ninth power
$2^{2}$	$2$ to the second	$2$ squared
$m^{3}$	$m$ to the third	$m$ cubed

Notice in the examples above that two special cases were included. When a number or variable is raised to the power of $2$ or $3,$ the exponential expression can be read as squared or cubed, respectively.

Exercise