What is Exponent Notation?

When we multiply the same number or letter by itself over and over, writing it out in full gets tedious very quickly. Exponent notation is a shorthand that makes this much neater.

Instead of writing $4 \times 4 \times 4$ , we write $4^{3}$ .

Base

The number or variable being multiplied repeatedly. In $4^{3}$ , the base is 4.

Exponent (Index / Power)

The small raised number that tells you how many times the base is multiplied by itself. In $4^{3}$ , the exponent is 3. It is also called the index or power.

So in the expression $a^{4}$ :

$a$ is the base
$4$ is the exponent
It means $a \times a \times a \times a$

Analogy

Think of the exponent like a "repeat" button on a music app. The base is the song, and the exponent tells you the total number of times to play it. $a^{4}$ means play $a$ exactly 4 times in a row — not 4 extra times, exactly 4 times total!

Reading and Speaking Exponent Notation

It's important to know how to read exponent expressions aloud. The table below shows the correct language using powers of 3 as examples:

Expanded Form	Exponent Notation	How to Say It
$3$	$3^{1}$	"3" or "3 to the power 1"
$3 \times 3$	$3^{2}$	"3 squared" or "3 to the power 2"
$3 \times 3 \times 3$	$3^{3}$	"3 cubed" or "3 to the power 3"
$3 \times 3 \times 3 \times 3$	$3^{4}$	"3 to the fourth" or "3 to the power 4"
$3 \times 3 \times 3 \times 3 \times 3$	$3^{5}$	"3 to the fifth" or "3 to the power 5"

Note

The special names "squared" and "cubed" only apply to powers of 2 and 3. For any other power, we say "to the power of ___".

Exam Tip

Any number or variable to the power 1 is just itself: $a^{1} = a$ . The expanded form of $3^{1}$ is simply $3$ — one instance of the base. You usually don't write the 1, but it's always there!

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