Visualizing Exponents in grade 9

We are working with areas and volumes and now starting to explore how exponents can represent areas and volumes.

For example, we’ll call one tooth pick x, then this is x squared.  The exponent tells us it will be 2 dimensional, and the base of the exponent is x, so that’s the dimension of the square.

It gets more complicated if we have different dimensions.  Here’s a square with side lengths of 2x.  The 2x has to be the base of the exponent, so we put it in brackets to show that.

Here’s (2x)^3 or 

We explored a wide variety of expressions that are 2 dimensional and 3 dimensional, with brackets and without.

Having a good visual understanding of what exponents mean will help later on!