12/12 -Exponent Laws Day 1

Multiple Choice

Which inequality best represents the domain of the part shown?

• $$-9<x\le2$$

• $$-9\le x\le2$$

• $$-6\le g\left(x\right)<3$$

• $$-6\le g\left(x\right)\le3$$

LO: SWBAT apply the properties of exponents to
simplify algebraic expressions with integral
exponents.

DOL: Given a set of problems, students will
correctly use the laws of exponents including
product rule, quotient rule, and zero exponent
rule to simplify algebraic expressions with
integral exponents in at least 4 of 5 questions.

A.11B: Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational
exponents.

2

Lesson Vocabulary

3

= 7 x 7 x 7

Exponents represent

Repeated multiplication.

7 times itself 3 times.

Understood 1
x = x

When a variable does not have a visible
exponent its exponent is understood to be 1.

1

Math

Tip

10

Zero Rule

a⁰

Any base with an exponent of zero is = 1

= 1

Proof

6³

6³

6³

6³

= (6・6・6)

(6・6・6)

= 1

18

​= 6^3-3= 6⁰=1

You can write a power as a product by writing out the repeated multiplication.

● “two to the seventh power.”

● “the seventh power of two.”

● “two raised to the seventh power.”

A Common mistake:

Why is this incorrect?

The exponent tells us how
many times we’re going to
multiply the base times itself.
The correct answer is 2⁷ = 128.

6

Math Response

What is the new exponent value of $$x^9\cdot x^7=x^?$$

without writing all the x's?

Type answer here

Correct Answer: 16

Deg^°

Rad

Fill in the Blank

What happens when we have two exponential expressions multiplying each other with the same base?

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Fill in the Blank

What happens when we have two exponential expressions dividing each other with the same base?

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Demonstration of Learning

DOL: Given a set of
problems, students
will correctly use the
laws of exponents
including product
rule, quotient rule,
and zero exponent
rule to simplify
algebraic
expressions with
integral exponents
in at least 4 of 5
questions.

24

Open Ended

How would you use expanded
notation to explain how an
exponent rule was developed?