Copyright © Swun Math Grade 8 Unit 2 Lesson 8 T TEMath Task
Unit 2 · Lesson 8: Explore Exponents
Directions: Explain why each statement is correct or incorrect. If needed, explain the error.
- Patty and Danny are discussing how to multiply expressions with the same base.
Patty says: 4^3 • 4^5 = 4^8 , because 3 + 5 = 8 and the base stays the same.
Danny says: 4^3 • 4^5 = 4^15 , because 3 • 5 = 15 and the base stays the same.Does either student know how to multiply expressions with the same base? Give a
clear explanation of how to work with exponents to resolve the discussion between
Patty and Danny.Solution:
Answers will vary. Sample response:
Patty is correct because 4^3 • 4^5 can be rewritten using expanded notation as
(4 • 4 • 4) • (4 • 4 • 4• 4 • 4), which is the same as 4^8.- Joey, Julian, and Austin are discussing how to multiply expressions with the same
exponent.
Joey says: 2^3 • 4^3 = 8^6 , because 2 • 4 = 8 and 3 + 3 = 6.
Julian says: 2^3 • 4^3 = 8^9 , because 2 • 4 = 8 and 3 • 3 = 9.
Austin says: 2^3 • 4^3 = 8^3 , because 2 • 4 = 8 and the exponent doesn’t change.Do any of the students know how to multiply expressions with the same exponent?
Give a clear explanation of how to work with exponents to resolve the discussion
between Joey, Julian, and Austin.Solution:
Answers will vary. Sample response:
Austin is correct because 2^3 • 4^3 can be rewritten using the distributive property (2 •4)^3 , which is 8^3.- State rules for multiplying expressions with the same base and multiplying expressions
with the same exponent.
Solution:
Answers will vary. Sample response:
When multiplying expressions with the same base, keep the base the same and add the exponents.
x^2 • x^3 = (x • x) • (x • x • x) = x^5When multiplying expressions with the same exponent, multiply the bases and keep the exponent the same.
x^3 • y^3 = (x • y)^3 = (xy)^3Name: ___
Date: ___