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Copyright © Swun Math Grade 8 Unit 2 Lesson 6 C TE

Convert Negative Exponents

Conceptual Lesson

Grade 8 · Unit 2 · Lesson 6
MC: 8 .EE. 1 

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Problem of the Day

Objective: I will use the reciprocal to convert negative exponents to positive.

Vocabulary Teacher Resources

Negative Exponent: indicates the number of

times to divide by the base

푥푥ି2

The negative sign says to do the inverse.

Dividing is the inverse of multiplying.

Reciprocal: what to multiply a value by to get 1;

multiplicative inverse

A negative exponent is equivalent to the inverse of the

positive of the same number.

xି3 is the reciprocal of x^3

4 ିହ is the reciprocal of 4 ହ

Properties of Exponents

Negative Exponent aି୬=ୟଵ౤

Considerations:

Review the chart from yesterday’s lesson to remind

students of the patterns between negative and

positive exponents. Allow time for discussion on the

use of multiplication when there is a positive

exponent and division when there is a negative

exponent (inverse relationship).

Review the concept that 52 and 5 –^2 are reciprocals.

• 52 means multiply 5 twice. 5^2 = 5 x 5 = 25


• 5 -2 means to do the exact opposite operation. So,
  instead of multiplying, divide.

5 -2 = ଵହ⋅ଵହ=2ହଵ=ହଵమ

Steps:

1. Identify the negative exponent.


2. Write the reciprocal.


3. Simplify.

Application of MPs:

MP 1 : How are negative exponents and reciprocals

related?

Negative exponents and reciprocals are

related because.

MP7: What is the relationship between xyand x−y?

The relationship between xyand x−yis that

they.

MPs

Applied MP

* Embedded MP

1 2 3 4 5 6 7 8

*  *

Student Journal Pages

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