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

Homework

Unit 2 · Lesson 6: Convert Negative Exponents

(^)
Objective: I will use the reciprocal to convert negative exponents to positives.
Vocabulary Steps:
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=
ଵ
ୟ౤^

1. Identify the negative exponent.


2. Write the reciprocal.


3. Simplify.

Example # 1 Example # 2

Directions: Write each expression using positive exponents.

2 ି3

Solution:

Use the patterns from yesterday’s chart or today’s

review of reciprocals.

• 2 ିଵ is equivalent to ଵ 2


• 2 ି2is equivalent to ଵ 2 ⋅ଵ 2 =ଵସ= 2 ଵమ


• Therefore 2 ି3 is equivalent to ଵ 2 ⋅ଵ 2 ⋅ଵ 2 =ଵ଼= 2 ଵ 3
  Answer: 2 ଵ 3

1

2 ି3

Solution:

• Identify that the denominator 2 ଵష3 can be rewritten using its
  inverse. ଵభ
  మ^3


• The fraction bar also represents a division. Rewrite as a
  division problem.
  1
  ଵ
  23

= 1 ÷

1

23

• Lastly, simplify by multiplying by its reciprocal:
  1 · 23
  Answer: 2^3

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