Lesson objective: Understand that by using patterns when we expand exponential expressions, we can derive rules/properties to write equivalent expressions.
Students bring prior knowledge of exponents from 6.EE.A.1. This prior knowledge is extended to deriving rules for writing equivalent expressions as students expand exponential expressions to write equivalent expressions when the base is the same. A conceptual challenge students may encounter is understanding that if the multiplying bases are the same, the base does not change as they write an equivalent expressions.
The concept is developed through work with a table showing expansions of exponent notation and patterns, which allows students to use the patterns to write their own rules for writing equivalent expressions (derive exponent properties).
This work helps students deepen their understanding of equivalence because students are writing rules to find equivalent expressions as numbers in exponential form are multiplied.
Students engage in Mathematical Practice 8 (look for and express regularity in repeated reasoning) as they multiply numbers written in exponential form and realize the product is always the same base and the sum of the exponents. A strategy students can use is expanding out expressions as a step in writing equivalent expressions.
Key vocabulary:

base

exponent

expression

factor

power
 product