# How do you write the verbal expression for 3^3?

May 1, 2016

"Three cubed" or "Three raised to the third power"

#### Explanation:

The analog of a square in different dimensions is:

$0$ - a point

$1$ - a line segment

$2$ - a square

$3$ - a cube

The measure (length, area, volume, etc.) of these analogs for an $n$-dimensional shape of side $a$ is:

$0$ dimensions (point): ${a}^{0} = 1$ - one object (points only have count, no dimension).

$1$ dimension (line segment): ${a}^{1} = a$ - length $a$

$2$ dimensions (square) ${a}^{2}$ - area $a$ squared

$3$ dimensions (cube) ${a}^{3}$ - volume $a$ cubed.

So in our example ${3}^{3} = 3 \times 3 \times 3 = 27$ is the volume of a cube of side $3$.