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

1 Answer
May 1, 2016

Answer:

"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 = 3xx3xx3 = 27# is the volume of a cube of side #3#.