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 Blanks

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

Drag and Drop

Question 1 = ​

Placeholder

Question 2 = ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Let's do #3 together...

Drag and Drop

Question 4 = ​

Placeholder

Question 5 = ​

Placeholder

Drag these tiles and drop them in the correct blank above

​Let's do #6 together...

Drag and Drop

​

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

Fill in the Blanks

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

Drag and Drop

Question 1 = ​

Placeholder

Question 2 = ​ ​

Placeholder

Drag these tiles and drop them in the correct blank above

Let's do #3 together...

Drag and Drop

​

Placeholder

​

Placeholder

​

Placeholder

Drag these tiles and drop them in the correct blank above

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?