12/12 -Exponent Laws Day 1

Multiple Choice

Simplify the expression 

$$\left(\frac{3m^2n^7}{m}\right)^5$$  

• $$81m^5n^{35}$$  

• $$243n^{35}m^5$$  

• $$243mn^{35}$$  

• $$15m^7n^{12}$$  

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

x⁻⁶

• 1 ⁄ x⁶
• x⁶
• -x⁶
• -1 ⁄ x⁶

Multiple Choice

Evaluate $$\frac{6n^2}{6n^{-2}}$$  

• $$n^4$$  

• $$\frac{1}{3n^{10}}$$  

• $$\frac{4}{3n^4}$$  

• $$4n^3$$  

Multiple Choice

Simplify $$\frac{5x^3}{2x^{-6}}$$  

• $$\frac{3x^4}{2}$$  

• $$x^9$$  

• $$\frac{5x^9}{2}$$  

• $$\frac{1}{3x^2}$$  

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

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

Fill in the Blank

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

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

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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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Anything with a power/exponent of zero equals 1!

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

Multiple Choice

Simplify (-1/2)⁰

• 1

• 0

• -1

• -2

Negative Exponent Rule

Negative exponents can be written as the reciprocal fraction with a postive exponent

Negative Exponent Rule

Multiple Choice

Simplify x^-7

• -7

• -7x

• 
  

  $$\frac{1}{x^7}$$

• $$-\frac{1}{x^7}$$
  

Multiple Choice

Make this negative exponent positive.

9^-3

• 9³

• $$\frac{1}{9^{-3}}$$

  
  

• $$\frac{1}{9^3}$$
  

• 729

Multiple Choice

Rewrite using positive exponents.

3x⁻²

• $$\frac{3}{x^2}$$

• $$\frac{1}{3^2}$$

• $$\frac{x^2}{3}$$
  

• -3x²

When you have an exponent raise to an exponent, MULTIPLY the exponents.

Multiple Choice

According to exponent rules, when we raise a power to another exponent we _______ the exponents.

• add
• subtract
• multiply
• divide

Multiple Choice

Simplify:

(x⁵)⁴

• x⁹

• x²⁰

• x

• x⁵⁴

Multiple Choice

(r⁴)⁶

• 10r
• r¹⁰
• 24r
• r²⁴

Multiple Choice

$$\left(3i^4\right)^3$$  

• $$15i^9$$  

• $$27i^{12}$$  

• $$15i^7$$  

• $$243i^9$$  

Multiple Choice

Simplify: $$8\left(x^4\right)^{\frac{1}{2}}$$  

• $$4x^2$$  

• $$8x^2$$  

• $$4x^4$$  

• $$8x^4$$  

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Multiple Choice

Simplify using the 9 Laws of Exponents:

Open Ended

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

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.

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