There is a great paradox in teaching math: the more simple a topic, the more likely it will cause complete confusion in your classroom. Cue – properties of exponents.
If you have experienced students mixing up all the laws of exponents or if you are about to teach them for the first time, then you are in the right place.
Laws of Exponents Standards
The standards are pretty clear. Note: In Texas, A.11B is a readiness standard, and this standard appeared twice in the 2024 STAAR. In fact, you can see below that in 2024, students were responsible for applying the law of product, law of quotient, law of power of a power, and negative exponents to simplifying a single expression.
In case you are rusty on what the laws of exponents are, let’s get on the same page:
To be extra clear, I would not recommend sharing the table above with your students when introducing the concept. The table could be used as an anchor chart or a cheat sheet during or at end of the unit which leads to me to my number one tip for teaching the laws of exponents:
TIP #1 PROPERTIES OF EXPONENTS → DISCOVERY LESSON
A discovery lesson will allow students to learn the laws of exponents through exploration, inquiry, and hands-on experiences rather than rote memorization. Instead of remembering to add exponents when powers with the same bases are multiplied, they can use expanded form to discover what happens to the exponent when powers with the same bases are multiplied.
We can turn to our MTM student handouts to see this modeled:
Present students with examples of the property in action and ask them to make observations about what is happening. Then you can formally introduce the property. In fact, by students discovering the laws, it puts them in a position to not ever have to memorize any of the laws because they can use the next tip –
TIP #2 EXPAND IT OUT
Expanded form is how your students will show their work for this skill. That means as you teach, model, solve, provide feedback, or grade, you will need to show expanded form or enforce that your students use it. I recommend giving students butcher paper with fun markers or whiteboards with dry erase markers to get them excited about expanded form.
Let’s say your students forget what the Quotient of Powers Property is and how to solve the problems below:
Even if you have never told students to subtract the exponents for this property, if students have practiced expanding the expression, and reducing the fraction by crossing off each set of variables that appear both in the numerator and denominator (because x÷x = 1), then they can apply the property. This goes for the Negative Exponent Property as well.
Tip #3 TWO WAYS TO HELP STUDENTS REMEMBER THE ZERO POWER PROPERTY
If your students are struggling with why a variable to the 0 power is 1, then there are two ways to help students understand. Provide a blank table and start with 4^3. Have students expand the expression and solve for 64. Then have them repeat for 4^ 2, 4^1, and 4^0. Ask students to observe what is happening to the standard form as the exponent decreases. Have students do it again with a different base to show that anything to a 0 power is 1.
(This table also reinforces the Negative Exponent Property.)
The next way to do this is to remind students that if the numerator and denominator are ever equal then it equals 1. You can start with 5/5=1.
TIP #4 RATIONAL NUMBER EXPONENTS – REVIEW, REVIEW, REVIEW
The rational number property requires more understanding beyond “expanding it out.” Students who can recognize squared and cubed numbers will be so much more successful here. Students who can multiply fractions fluently will also benefit! Reviewing previously learned concepts prior to introducing rational number exponents will pay off dramatically.
Scope and Sequence/Pacing
For the best outcome, I would recommend introducing the laws of exponents to students over the course of about 4-5 days. Here is how I would do it:
Day 1 and 2 – Properties of Exponents: Multiplication
Here you can cover the Product of Powers Property, the Power of a Power Property, and the Power of a Product Property. I would spend 1-2 days depending on how long class periods are.
Day 3 and 4 – Properties of Exponents: Division
Here you will tackle the Quotient of Powers Property, the Negative Exponent Property, and the Zero Power Property. Again, I would spend about 1-2 days on these laws based on your class period length.
Day 5 and 6 – Rational Exponents
There is only one property – the Rational Exponent Property to tackle on this day, but remember that you may need to review square and cube roots.
To put it all together, here is what my scope and sequence would like based on my 75 minute class, and full access to all the resources that All Access has to offer:
Shop: Maze Activity | Puzzle Train Activity | Properties of Exponents Digital Activity are included in Algebra 1 All Access
OTHER TIPS
- If you are an All Access member, you can filter the unit resources by activity to see all of the activities available. I would highly recommend utilizing activities to supplement instruction!
- Need a reminder for having students move negative exponents to the denominator? NEGATIVES NAVIGATE! You can also have them brainstorm stories that will remind them of this rule.
- Read more tips for teaching Exponents and Scientific Notation
How do you teach the laws of exponents?
