Index notation with integer and variable bases

Common Indices

The terms indices (or indexes) and 'powers' refer to the same thing.

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

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

When we talk about indices, it is important to remember the difference between the index and the base.

For example, in $10^3$103, $10$10 is the base number and $3$3 is the index number:

Hint: Think of the 'base' as that being closest to the ground, and the index is 'in' the air.

 

Examples

Question 1

Question 2

 

Question 3