Curriculum / Math / 8th Grade / Unit 1: Exponents and Scientific Notation / Lesson 8
Math
Unit 1
8th Grade
Lesson 8 of 15
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Lesson Notes
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Reason with negative exponents to write equivalent, simplified exponential expressions.
The core standards covered in this lesson
8.EE.A.1 — Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3² × 3<sup>-5</sup> = 3<sup>-3</sup> = 1/3³ = 1/27.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
A common error when working with negative exponents is to over-apply the rule to bases that have an implicit exponent of 1 or to negative numbers (not exponents). For example, $${2x^{-1}}$$ is often incorrectly written as $${1\over{2x}}$$ , not realizing that the base 2 has a positive exponent of 1 and should remain in the numerator.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
25-30 minutes
What is the value of $${{{{{5^{-2}}}}}}$$? 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 $${{{{{5^{-2}}}}}}$$?
$${5^2}\cdot{{{{{5^{-2}}}}}}=5^{2+(-2)}={5^0}=1$$
Strategy 2: Use quotient of power rule
$${5^4\over5^6}={{5\cdot5\cdot5\cdot5}\over{5\cdot5\cdot5\cdot5\cdot5\cdot5}}=5^{4-6}={{{{{5^{-2}}}}}}$$
Strategy 3: Use a table
Complete the table below to shed light on the value of $${{{{{5^{-2}}}}}}$$.
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Simplify the following expressions to the fewest number of bases possible and no negative exponents.
a. $${15^4\over{15^{-3}}}$$
b. $${2x^{-5}}$$
c. $${(ab^2)^{-3}}$$
d. $${m^{-3}\over m}$$
e. $${\left ({1\over3} \right )^{-2}}$$
f. $${1\over{7^{-8}}}$$
A set of suggested resources or problem types that teachers can turn into a 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.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
The expressions in each example below are not equivalent. Explain a possible mistake that could have been made and then find an equivalent expression.
a. $${{x^{-3}y^2\over{y^{-4}x^2}}={1\over{y^6x^5}}}$$
b. $${4m^{-1}={1\over{4m}}}$$
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.
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Simplify and write equivalent exponential expressions using all exponent rules.
Topic A: Review of Exponents
Review exponent notation and identify equivalent exponential expressions.
Standards
8.EE.A.1
Evaluate numerical and algebraic expressions with exponents using the order of operations.
Investigate patterns of exponents with positive/negative bases and even/odd bases.
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Topic B: Properties of Exponents
Investigate exponent patterns to write equivalent expressions.
Apply the product of powers rule and the quotient of powers rule to write equivalent, simplified exponential expressions.
Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.
Reason with zero exponents to write equivalent, simplified exponential expressions.
Topic C: Scientific Notation
Write large and small numbers as powers of 10.
8.EE.A.38.EE.A.4
Define and write numbers in scientific notation.
8.EE.A.3
Compare numbers written in scientific notation.
Multiply and divide with numbers in scientific notation. Interpret scientific notation on calculators.
8.EE.A.4
Add and subtract with numbers in scientific notation.
Solve multi-step applications using scientific notation and properties of exponents.
8.EE.A.18.EE.A.38.EE.A.4
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