# Lesson 18

Bases and Exponents

These materials, when encountered before Algebra 1, Unit 5, Lesson 18 support success in that lesson.

### Lesson Narrative

In the associated Algebra 1 lesson, students examine different ways to express repeated percent increase. Here, they have an opportunity to do similar work with numbers that are easier to work with mentally. By understanding how the meaning of exponents and the property \((x^a)^b = x^{ab}\) can be used to rewrite numerical expressions, they will be able to use structure that they notice here in the work in the Algebra 1 lesson. In the activity “Rewriting Expressions”, students practice using the property \((x^a)^b=x^{ab}\) to rewrite expressions. This practice will put them in a better position to explain why expressions are equal and write equivalent expressions in the associated Algebra 1 lesson. When students notice that they can rewrite an expression by substituting an equal expression or using a property, they are noticing and making use of structure (MP7).

### Learning Goals

Teacher Facing

- Identify and create equivalent expressions using the property $(x^a)^b = x^{ab}$.

### Student Facing

- Let’s rewrite expressions using the property \((x^a)^b = x^{ab}\).