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


Problem 1

Is the following statement true? Show your reasoning.

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

Guiding Questions

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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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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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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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Problem Set

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Target Task


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?
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Lesson 5

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Lesson 7

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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