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Copyright © Swun Math Grade 8 Unit 2 Lesson 7 P TE

Homework

Unit 2 · Lesson 7: Zero and Negative Exponents

Objective: I will evaluate expressions with zero 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. Write the expression in expanded form.


2. Simplify by canceling common factors.


3. Rewrite exponent as a positive exponent.
   OR


4. Subtract exponents of like bases.


5. Write answer using positive exponent.

Example # 1 Example # 2

Directions: Simplify the expression. Write solution using a positive exponent.

6 −^8 ⋅ 68

Solution

1 st Strategy

• 6 −8+8(Keep in mind the rules for adding integers.)


• 60 = 1

2 nd Strategy

● Change each number so they have positive

exponents.

● 618 ⋅ 68

● 6

8

68

● 60 = 1

3 푥푥^5 ⋅ 푥푥−^2

푥푥^4

Solution:

1 st Strategy

The bases are the same, so add the exponents in the numerator

and then subtract with the exponents that have the same base

in the denominator.

• 3푥푥

3

푥푥^4 = 3⋅푥푥

3−4(Students might want to write 4 – 3)

• 3 ⋅푥푥−1=^3 푥푥

2 nd Strategy

Use expanded form and cancel the common factors.

• 3⋅푥푥⋅푥푥⋅푥푥⋅푥푥⋅푥푥⋅푥푥

−1⋅푥푥−1

푥푥⋅푥푥⋅푥푥⋅푥푥 C hange the two negative exponents so they

are positive.

• 31 ∙푥푥푥푥∙푥푥푥푥∙푥푥푥푥∙푥푥푥푥∙푥푥푥푥∙^1 푥푥→^31 ∙^1 푥푥


• 31 ⋅^1 푥푥=^3 푥푥

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