Exponents and Scientific Notation

Lesson 6

Math

Unit 1

8th Grade

Lesson 6 of 15

Objective


Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.

Common Core Standards


Core Standards

  • 8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3-5 = 3-3 = 1/3³ = 1/27.

Criteria for Success


  1. Investigate, determine, and apply the general rule for power of product: $${(xy)^m = x^my^m}$$.
  2. Investigate, determine, and apply the general rule for power of powers$${(x^m)^n=x^{mn}}$$.
  3. Know that $${\left ( x+y \right )^{m} \neq x^m+y^m}$$.

Tips for Teachers


  • In terms of pacing, this lesson may be split over more than one day.
  • Similar to Lesson 5, these Anchor Problems can be used in a variety of ways, including having students lead the discovery and seek out a general rule. 
  • Once students have experimented with the problems and found a generalization, then provide them with the name of the rule and the general form.
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Anchor Problems

25-30 minutes


Problem 1

Is the following statement true? Show your reasoning.

$${4^53^5=12^5}$$

Guiding Questions

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Student Response

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Problem 2

Write an equivalent form of each of the following:

a.   $${(4x)^5}$$

b.   $${(-3mn)^2}$$

c.   $${\left ({5x\over y} \right )^3}$$

Guiding Questions

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Student Response

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Problem 3

Lucas thinks that since $${(ab)^2 = a^2b^2}$$, then that must mean $${(a+b)^2 = a^2+b^2}$$. Is Lucas’ reasoning correct? Explain or show why or why not.

Guiding Questions

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Student Response

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Problem 4

How is $${7^27^6}$$ different from $${(7^2)^6}$$? What is an equivalent expression for each one? 

Use your reasoning to simplify the following:

a.    $${(11^5)^4}$$

b.    $${-(2^3)^6}$$

c.    $${((-1)^3)^{12}}$$

Guiding Questions

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Student Response

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Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Simplify the following expressions:

a.   $$(2^5)^7$$

b.   $$(91^3\times 19\times 103^8)^4$$

c.   $$(p^4q^5r)^9$$

d.   $$2^7\over 3^7$$

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include a mixture of problems that involve using all the rules learned so far.
  • Revisit the worksheet from Lesson 4, before students learned the more general approaches and rules. Do any of the problems illustrate the rules you’ve learned?

Next

Reason with zero exponents to write equivalent, simplified exponential expressions.

Lesson 7
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Review of Exponents

Topic B: Properties of Exponents

Topic C: Scientific Notation

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