Exponent Laws Introduction

Today grade 9s were working hard to represent multiplication in many ways. Here’s a sequence of questions that led us to the exponent law for multiplying.

Represent 4 times 2 times 3:

Students showed in many ways that they understood what (4)(2)(3) is.

Represent 3 squared.

Following what we did yesterday, we know that the exponent 2 means to make a square. The side lengths are 3. We know we can write (3)(3) in many ways as well.

Represent 4 cubed:

It will take 64 little cubes to build a 4x4x4 cube.

Represent x squared.

Represent 2x^3

2(x)(x)(x) is another way to show it.

Represent 2x^3y^4

Represent 1/2x^4z^2p^3

We noticed that there is a hidden multiplication between all the letters.

Represent (x^4)(x^2)(x^3)

We can see so many (x) multiplied together, and we can represent this as x^9. When we multiply and the bases are the same we can add the exponents.

This next question was more challenging because we now have coefficients involved.

(-4)(x)(x)(x)(y)(y)(-2)(x)(y)(y)(y)(y)

this can be written as (-4)(-2)(x)(x)(x)(x)(y)(y)(y)(y)(y)(y) since the order doesn’t matter when we multiply.

It was a busy fun class today! Well done grade 9s.