Mathematical Powers – a Simple IllustrationLet’s consider the example of three times three. That can be written either 3 x 3 = 9, or in powers notation,
3² = 9This tells us three to the second power (or three squared) equals nine. Consider the two images associated with this article. One is a square with sides equal to 3. The other is a cube with its three sides each equal to 3 as well. The former square contains within it nine 1 x 1 inch smaller squares. The cube contains within it twenty-seven 1 x 1 x 1 smaller cubes.
I know of no one who can draw a geometrical figure that demonstrates the mathematical powers expression 3⁴ = 3 x 3 x 3 x 3 = 81. But we should need no such figure. The simple insight we’ve provided using the square and the cube should suffice.
One Last ThoughtFor one last help, one last aid, consider this. 3² = 3 x 3. And 3³ = 3 x 3 x 3. In the first case, the power 2 also represents the number of 3’s that are multiplied together. In the second case, the power 3 represents a similar thing. So the multiplication power expression 3⁸ consists of eight 3’s multiplied times each other, or
3⁸ = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 = 6561References: ← Back to Math-Logic-Design