Indices

NZ Level 5

Index notation revision

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.

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 $x^2$`x`2, 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 $x^3$`x`3, 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 $x^n$`x``n` 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.

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

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

$6$6

A$4$4

B$6$6

A$4$4

B

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

$5^{-13}$5−13

A$-5^{13}$−513

B$-5^{-13}$−5−13

C$5^{13}$513

D$5^{-13}$5−13

A$-5^{13}$−513

B$-5^{-13}$−5−13

C$5^{13}$513

D

Use prime numbers, common factors and multiples, and powers (including square roots)