Proofs of Laws of Exponents

Examples, solutions, and videos to help Grade 8 students learn to extend the previous laws of exponents to include all integer exponents

New York State Common Core Math Grade 8, Module 1, Lesson 6.
Worksheets for Grade 8

Lesson 6 Student Outcomes

• Students extend the previous laws of exponents to include all integer exponents.
• Students base symbolic proofs on concrete examples to show that (x^b)^a = x^ab is valid for all integer exponents.

The Laws of Exponents

For x, y > 0 and all integers a, b the following holds:
x^a • x^b = x^{a + b}
(x^b)^a = x^ab
(xy)^a = x^ay^a

Lesson 6 Problem Set Solutions

1. You sent a photo of you and your family on vacation to seven Facebook friends. If each of them sends it to five of their friends, and each of those friends sends it to five of their friends, and those friends send it to five more. How many people (not counting yourself) will see your photo? No friend received your photo twice. Express your answer in exponential notation.

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