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AIM: How do we apply the laws of exponents (product, power, quotient, and zero rules)?

Take two minutes to get your Do­Now and Signals before we begin today's lesson.

Do­Now Begins!

Independent Thinking and Work: Partner Share and Discussion:

A l e r t ! Alert!

Finished ? Write down the homework.

HOMEWORK

1) HW 1.1 Q#11 ­ 18 Due Tomorrow

Do­Now Review

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Do­Now Review

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Do­Now Review

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Do­Now Review

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Announcements: 1) Seating chart starts next Monday 2) Turn in contracts and surveys. (Supplies due this Friday) 3) Pre­Regents Exam next week Monday & Tuesday

Look at the completed problems below, and discuss a shortcut that works for ALL of them.

Use your shortcut to simplify this expression:

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Multiplying Exponents

Multiplying exponents with the same base RULE: ADD THE EXPONENTS

What is the shortcut?

x3x2x5

(x x x) (x x) (x x x x x)

Use Commutative Property

x3 (x5) = x8

and Multiply the Coefficients

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

(x2)(x3)

(x­3)(x4)

­3m5 (7m)

2x3y (11x5y4)

Try it yourself 1)

Simplify each expression

2) 3)

4)

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

CW 1.1 ­ Try it!

(x2)(x3)

(x­3)(x4)

­3m5 (7m)

2x3y (11x5y4)

Try it yourself 1)

Simplify each expression

2) 3)

4)

4 Correct 0 ­ 1 Correct 2 ­ 3 Correct

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

How about dividing???

Look at the completed problems below, and discuss a shortcut that works for ALL of them.

Use your shortcut to simplify this expression:

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Dividing Exponents

Dividing exponents with the same base RULE: SUBTRACT THE EXPONENTS

x6 x2 = x4

What is the shortcut?

and Divide the Coefficients

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

CW 1.1 ­ Try it!

5)

Simplify each expression

6) 7)

8)

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Try it yourself

5)

Simplify each expression

6) 7)

8)

4 Correct 0 ­ 1 Correct 2 ­ 3 Correct

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Raising a Power to a Power

(22)3 (c3)4

Exponential Form

Expanded form

Completely Expanded Form

Simplified

Use your shortcut to simplify this expression:

Look at the completed problems below, and discuss a shortcut that works for ALL of them.

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Raising a power to a power RULE: MULTIPLY THE EXPONENTS and Raise the Coeffient to the Power or Exponent

(ab)c = abc

What is the shortcut?

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

CW #11 ­ Try it!

9)

Simplify each expression

10) 11)

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Try it yourself

9)

Simplify each expression

10) 11)

3 Correct 0 ­ 1 Correct 2 Correct

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

12)

Two interesting things appear in this problem using the shortcut: 1) an exponent of zero 2) a negative exponent What do they really mean????

First method of understanding:

Looking at a pattern

Let's Take a Closer Look at #12

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Zero Exponents

x x5

5

x x x x x x x x x x

x0

x5­5

= = = =

x x5

5

1

=

­or­

Zero as an exponent: a0=1

1

=

x x7

2

= x­5

x2­7

Answers with negative and/

• r zero exponents

are NOT simplified!

­or­

x x7

2

=

x x x x x x x x x

=

1 x x x x x =

1

x5

=

a­n

1 an

x­5

1 x5

=

Negative Exponents Second method of understanding:

Using Variables and expanded form

This is the key

touch

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

• Ex. 1

CW #13 CW #14

Simplifying Zero Exponents

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

CW #13 CW #14

Simplifying Zero Exponents

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

• Ex. 1
• Ex. 2

CW # 15

Simplifying Negative Exponents

CW #16 CW #17

• Ex. 3

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

CW # 15

Simplifying Negative Exponents

CW #16 CW #17

• Ex. 3

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

• Ex. 4

As a Class With Your Partner Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

• Ex. 10

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Exit Ticket!

1)

2)

Simplify each expression.

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

1)

2)

Simplify each expression.

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Simplify using only positive exponents.

Exit Ticket!

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

Simplify using only positive exponents.

Exit Ticket

Aim: How do we apply the laws of exponents (product, power, quotient, and zero rules)? HW: Worksheet 1.1

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