Exponents and Scientific Notation

Lesson 7

Math

Unit 1

8th Grade

Lesson 7 of 15

Objective


Reason with zero exponents 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 zero exponents: $${x^0=1}$$ for non-zero numbers.
  2. Simplify exponential expressions using exponent rules.

Tips for Teachers


The question of what is the value of $${{0^0}}$$ may come up. There is not a definitive answer to this, as there are valid reasons to believe that it equals 1, and there are valid reasons to believe it equals 0 (involving some math beyond 8th grade). It is common to say that $${{0^0}}$$ is undefined.

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Anchor Problems


Problem 1

What is the value of $${{{{{5^0}}}}}$$? Explore 3 different strategies to determine the value.

Strategy 1: Use product of powers rule
How does the statement below shed light on the value of $${{{{{5^0}}}}}$$?

$${5^{2}\cdot 5^{0}=5^{2+0}=5^{2}}$$

Strategy 2: Use quotient of power rule
How does the statement below shed light on the value of $${{{{{5^0}}}}}$$?

$${{5^2}\over{{5^2}}}=5^{2-2}={{{{{5^0}}}}}$$

Strategy 3: Use a table
Complete the table below to shed light on the value of $${{{{{5^0}}}}}$$.

Exponent Value
$${5^3}$$  
$${5^2}$$  
$${5^1}$$  
$${{{{{5^0}}}}}$$  

Guiding Questions

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Problem 2

Which is bigger, one raised to the millionth power or one million raised to the zeroth power?

Guiding Questions

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Problem Set

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Target Task


Problem 1

Which expressions below are equivalent to 1? Select all that apply.

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Problem 2

What is the value of $$n$$ in the equation below? Explain your answer.

$${2^n\cdot{2^3\over{2^5}}=1}$$

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 mix of problems that incorporate the previous properties learned.
  • Challenge: Write an exponential expression using at least 3 different bases and at least one set of parentheses that simplifies to 1.
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Lesson 6

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Lesson 8

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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