Exponents Beyond 10: Other Bases and Rational Numbers

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7th Grade (Accelerated)Building Thinking Classrooms50 min

Learning Objective

Students will apply the properties of exponents (product rule, quotient rule, power rule) to expressions with integer, negative, and rational bases, and evaluate or simplify such expressions.

Lesson Overview

Students discover and apply exponent rules (product, quotient, power) using bases other than 10, then extend to rational number bases including fractions and negative numbers. Tasks thin-slice from integer bases to rational bases, building toward fluency with all base types.

Materials

Vertical whiteboards or large chart paper
Dry-erase markers (multiple colors)
Pencils and paper
Basic calculator or phone calculator (for checking only)

Scaffolded Task Progression

1Task 1

Write

3^{4}

as repeated multiplication and find its value. Then write

3^{2} \cdot 3^{3}

as repeated multiplication and find its value. What do you notice? Write a rule in words.

2Task 2

Use the product rule to simplify each expression. Do NOT expand — just apply the rule. Then verify one of your answers by expanding.
a)

5^{3} \cdot 5^{4}

7^{2} \cdot 7^{5}

4^{6} \div 4^{2}

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