# Lesson 15

Equivalent Exponential Expressions

### Lesson Narrative

In this lesson, students encounter expressions and equations with variables that also involve exponents. Students first evaluate expressions for given values of their variables. They learn that multiplication can be expressed without a dot or other symbol by placing a number, known as a coefficient, next to a variable or variable expression. In the next activity, students are presented with equations that contain a variable. They engage in MP7 by considering the structure of the equations and apply their understanding of exponents and operations to select a number from a list that, when replaced for the variable, makes the equation true. That number is a solution of the equation.

### Learning Goals

Teacher Facing

• Describe (orally) the values that result from evaluating expressions in which a fraction is raised to a power.
• Determine whether a given value is a solution to an equation that includes an exponent.
• Evaluate expressions that have a variable, an exponent, and one other operation for a given value of the variable, carrying out the operations in the conventional order.

### Student Facing

Let's investigate expressions with variables and exponents.

### Student Facing

• I can find solutions to equations with exponents in a list of numbers.
• I can replace a variable with a number in an expression with exponents and operations and use the correct order to evaluate the expression.