Laws of Exponents:Product and Quotient Rule

​LAWS OF EXPONENTS

​Weekly Objective: Students will use reasoning to define the laws of exponents to simplify expressions with exponents by applying the including:

----Product Rule
----Quotient Rule
--Power Rule

with an at least 75% accuracy.

True Meaning of Exponent

Discussion Question: How can knowing the growth of smart phone sales be an asset to businesses? Give an example.

​

Exponents in Our World

Growth of Smart Phones Affect:

My Example

The Smart Phone Company: it can provide actionable insights into a sales team's performance, help them build better strategies, and improve organizational decision-making to handle the demand of the product and continue to grow demand.

Vocabulary Review

Base:
a number that is raised to a certain power

Exponent:
Shows how many times the number is multiplied by itself.

Coefficient:
a number that multiplied by the variable

Multiple Choice

What is the base in the term: $$4x^2$$

• x

• 2

• 4

• $$4x^2$$

Multiple Choice

Pick the best option: Has a base of 5 and an exponent 7.

• $$7^5$$

• $$5x^7$$

• $$5^7$$

• $$7x^5$$

Open Ended

Create an expression where

Coefficient is 6 the base is y and the exponent is 5

Open Ended

Create an expression with a coefficient less than 5 and an exponent more than 10.

Multiple Choice

Pick the answer choice that label parts of the term correctly:

$$6y^9$$

• Coefficient: y

  Base: 6

  Exponent: 9

• Coefficient: 9

  Base: 6

  Exponent: y

• Coefficient: y

  Base: 6

  Exponent: 9

• Coefficient: 6

  Base: y

  Exponent: 9

Exponents

Let's review exponents!

Open Ended

Expand and simplify $$4^5$$ Fill in on table

Open Ended

Expand and simplify $$6^3$$

Multiple Choice

$$x^6$$

• $$x\times x\times x\times x\times x\times x$$

• $$6\times6\times6\times6\times6\times6$$

• $$6\times x$$

• $$6\times x\times x\times x\times x\times x$$

Today's Objective

Today we will learn to simplify expressions by applying the laws of exponents when it comes to multiplication (product rule) and division(quotient rule)

Product Rule: Investigation

Could you create a rule to simplify the expression?

Rule: 

Product Rule: Investigation

Product Rule

Multiple Choice

Simplify:
(b² )(b⁴)

• b⁸
• b⁶
• b²
• 2b⁶

Multiple Choice

$$b^3\times b$$

• $$b^3$$

• 
  $$b^4$$

• $$b^2$$

• $$2b^3$$

Multiple Choice

$$n^{ }⋅n⁴⋅n⁵$$

• $$n^9$$

• $$n^{20}$$

• $$n^{10}$$

• $$n^{45}$$

Multiple Choice

Multiply: (X²Y⁴) (X⁵Y¹²)

• X⁷Y¹⁶
• X¹⁰Y⁴⁸
• X^-3Y^-8

Multiple Choice

9n⁴ . 6n⁷

• 15n¹¹
• 54n²⁸
• 3n³
• 54n¹¹

Multiple Choice

Simplify the following expression:

3x⁴ ⋅ 6x⁶

• 18x¹⁰

• 9x¹⁰

• 18x²⁴

• 9x²⁴

Multiple Choice

Simplify:  (5p⁹q³)(2pq⁷)

• 7p¹⁰q¹⁰
• 10p⁹q²¹
• 10p¹⁰q¹⁰
• 10p⁸q^-4

Multiple Choice

Simplify the following expression:

2x³y⁵ ⋅ 5xy²

• 10x⁴y⁷

• 7x⁴y⁷

• 10x³y¹⁰

• 7x³y¹⁰

Quotient Rule: Investigation

Could you create a rule to simplify the expression?

Rule: 

Quotient Rule: Investigation

Quotient Rule

Multiple Choice

$$\frac{x^5}{x^2}$$  

• $$x^3$$  

• $$x^{10}$$  

• $$x^3$$  

• $$\frac{1}{x^3}$$  

Multiple Choice

Simplify the expression.

• y¹⁵
• y⁵⁰
• y²
• y⁵

Multiple Choice

$$\frac{12x^5}{4x^2}$$

• 3x
• 3x⁷
• 3x³

Multiple Choice

$$\frac{x^3\cdot x^4}{x^2}$$  

• $$\frac{x^7}{x^2}$$  

• $$\frac{1}{x^{10}}$$  

• $$x^5$$  

• $$x^{-5}$$