Middle Years

# 1.06 Powers of whole numbers

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 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, e.g. $5$5 with an index (or power) of $2$2, can be expressed as $5^2$52, and can be read as "$5$5 to the power of $2$2" or "five squared".

A number, e.g. $10$10 to the power of $3$3, can be expressed as $10^3$103, and can be read as "ten cubed". A power of $3$3 is involved in calculations like measuring the volume of a cube.

Base and power

A base to the power of any other number, e.g. $3^4$34, can be read as "three to the power of four", and means that the base number is multiplied by itself the number of times shown in the power.

$3^4=3\times3\times3\times3$34=3×3×3×3

The following demonstration illustrates more of this notation. Try varying the bases and exponents (by moving the sliders) to see how the numbers change.

 Created with Geogebra

#### 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

Evaluate $\frac{3^5}{3^3}$3533.