Curriculum / Math / 8th Grade / Unit 1: Exponents and Scientific Notation / Lesson 5
Math
Unit 1
8th Grade
Lesson 5 of 15
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Apply the product of powers rule and the quotient of powers rule 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
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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
Write an equivalent, simplified form of each of the following:
a. $${6^3\times6^5}$$
b. $${\left (-{1\over4} \right )^4\left (-{1\over4} \right )^3}$$
c. $${12^a\cdot 12^b}$$
d. $${x^mx^n}$$
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a. $${5^3\cdot 25\cdot 5^4}$$
b. $${5^63^2\times3\times5^3}$$
c. $${(2xy)(x^2y^3)(2y^4)}$$
a. $${8^6\over8^3}$$
b. $${{\left (-{1\over2} \right )^9}\over{\left (-{1\over2} \right )^5}}$$
c. $${\frac{6^{4}5^{7}}{6\cdot 2^{5}}}$$
d. $${x^m\over x^n}$$, where ($$m > n$$)
Your teacher writes the following two expressions on the board:
Your teacher asks the class if these two expressions are equivalent. Half of the class says yes, and half says no. What do you think? Convince the other half of the class that you are correct.
Exponent Rules are Lame is made available on Nathan Kraft's Blog. Accessed Aug. 4, 2017, 10:11 a.m..
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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.
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5-10 minutes
Simplify the following expressions.
a. $$17^x(17^y)$$
b. $$2^4(32)$$
c. $$5^a\over 5^b$$
d. $$3^6÷27$$
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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Apply the power of powers rule and power of product rule to write equivalent, simplified exponential expressions.
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.
Reason with zero exponents to write equivalent, simplified exponential expressions.
Reason with negative exponents to write equivalent, simplified exponential expressions.
Simplify and write equivalent exponential expressions using all exponent rules.
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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