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Copyright © Swun Math Grade 8 Unit 2 Lesson 5 C TE

Homework

Unit 2 · Lesson 5: Properties of Exponents:
Zero & Negatives

Objective: I will explore patterns with positive and negative exponents.

Vocabulary Steps:

Negative Exponent: indicates the number of

times to divide by the base

푥푥−2

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.

x−3 is the reciprocal of x^3

4 −5 is the reciprocal of 45

(^)
Properties of Exponents
Zero Exponent a^0 = 1
Negative Exponent a−n=a^1 n

1. Complete the chart.


2. Use expanded form to identify the standard
   notation.


3. Identify the pattern.


4. Use the pattern to identify the standard notation.

Example # 1 Example # 2

Directions: Use pattern reasoning to find the expanded and standard form.

Solution:

• Using the pattern established, determine that since 2^1 =
  2, 2 will be divided by the base to yield the value of 2^0.


• 2 ÷ 2 = 1. Therefore, 2^0 = 1

Power Expanded Form Standard Form

24 2 ⋅ 2 ⋅ 2 ⋅ 2 16

23 2 ⋅ 2 ⋅ 2 8

22 2 ⋅ 2 4

(^21 2 2)
(^20 1 1)
Solution:

• 12 =÷^12. Therefore,^2 −^1 = 21


• Continue the pattern to find 2 −2 and 2 −3.


• 
  

(^112)
24
÷=. Therefore 22 1
4
− =

• 1148 ÷= 2. Therefore 2 −^3 = 81

Power Expanded Form Standard Form

23 2 ⋅ 2 ⋅ 2 8

22 2 ⋅ 2 4

21 2 2

20 1 1

2 −1 1

2

1

2

2 −2 (^12) ⋅^12 1
4
2 −3 (^12) ⋅^12 ⋅^12 1
8
Name:
Date:
1
4 ÷ 2^
(^1) ÷ 2
1
2 ÷ 2^