# Index notation

Lesson

An index (or power) is a small number placed in the upper right hand corner of another number to note how many times a base number is being multiplied by itself.

For example, in the expression $10^3$103 the number $10$10 is the base term and the number $3$3 is the index (or power) term. The expression $10^3$103 is the same as $10\times10\times10$10×10×10, or the number $10$10 multiplied $3$3 times.

Think of the base as that being closest to the ground, and the index (or power) is above.

We often encounter a power of $2$2 when measuring area. Consider the area of a square, for example, which is given by side length times side length. A number $x$x with an index (or power) of $2$2, can be expressed as $x^2$x2, and is often read as "$x$x to the power of $2$2" (or "$x$x squared").

A number $x$x to the power of $3$3, which can be expressed as $x^3$x3, is also known as "$x$x cubed". A power of $3$3 is involved in calculations like measuring the volume of a cube.

To summarise

A base number $x$x to the power of any other number $n$n, can be expressed as $x^n$xn and can be read as "$x$x to the power of $n$n".

Did you know?

The terms indices, exponents, powers, and orders are all different terms used to mean the same thing.

#### Practice questions

##### Question 1

State the base for the expression $3^2$32.

##### Question 2

Identify the power for the expression $4^6$46.

1. $6$6

A

$4$4

B

$6$6

A

$4$4

B

##### Question 3

$\left(-5\right)^{13}$(5)13 simplifies to which of the following?

1. $5^{-13}$513

A

$-5^{13}$513

B

$-5^{-13}$513

C

$5^{13}$513

D

$5^{-13}$513

A

$-5^{13}$513

B

$-5^{-13}$513

C

$5^{13}$513

D