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Visualizing Exponents in grade 9

March 20, 2019

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!

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