Hart Interactive – Algebra 1 M1 Lesson 6A ALGEBRA I

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations Exploratory Activity

1. A. With your partner, fill in the table below about exponents and then describe the Product Rule.

Expression Repeated Multiplication Simplified Form

2 43 3 3< <

4 2 34 4 4< <

6 39 9<

7 9 2a a a< <

B. The Product Rule for Exponents: m na a =< ___________

2. A. With your partner, fill in the table below about exponents and then describe the Division Rule and Negative Exponent Rule.

Expression Repeated Multiplication Simplified Form

2

433

4

344

3

699

17

9aa

B. The Division Rule for Exponents: m

n

xx

= __________

C. The Negative Exponent Rule: mx− = ____________

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations

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Hart Interactive – Algebra 1 M1 Lesson 6A ALGEBRA I

3. With your partner, fill in the table below about exponents and then describe the pattern you see.

Expression with Exponents

Simplified Expression without Exponents

23

22

21

20

2-1

2-2

4. A. With your partner, fill in the table below about exponents and then describe the Zero Exponent Rule.

Expression Repeated Multiplication Simplified Form

4

433

3

344

6

699

9

9aa

B. The Zero Exponent Rule: 0x = _________, x ≠ 0.

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations

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Hart Interactive – Algebra 1 M1 Lesson 6A ALGEBRA I

5. A. With your partner, fill in the table below about exponents and then describe the Power of a Product or Quotient Rule.

Expression Repeated Multiplication Simplified Form

( )23 2<

( )35 3<

( )5abc

( )42x

6ac

B. The Power of a Product or Quotient Rule for Exponents: ( )mxy = ___________ and m

xy

__________

6. A. With your partner, fill in the table below about exponents and then determine the Power to a Power Rule.

Expression Repeated Multiplication Simplified Form

( )243

( )325

( )53 2ab c

( )422x

62

3ac

B. The Power to a Power Rule for Exponents: ( )nmx = ____________

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Hart Interactive – Algebra 1 M1 Lesson 6A ALGEBRA I

Lesson Summary

Rules for Exponents

Product Rule ______m na a a=< Zero Exponent

Rule 0 _____a =

Division Rule ______m

na aa

= Power of a Product

Rule ( ) _____na b =<

Power of a

Quotient Rule ma

b=

Negative Exponent Rule

______1n a

a= Power to a Power

Rule

nm

pab

= and ( ) _____nm pa b =<

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations

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This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Hart Interactive – Algebra 1 M1 Lesson 6A ALGEBRA I

Homework Problem Set 1. Think about order of operations to insert parentheses to make each statement true. If you are having

trouble remembering the Order of Operations, watch the YouTube video by Math Antics https://www.youtube.com/watch?v=dAgfnK528RA. A. 2 + 3 × 42 + 1 = 81 B. 2 + 3 × 42 + 1 = 85 C. 2 + 3 × 42 + 1 = 5 D. 2 + 3 × 42 + 1 = 53

2. Simplify each expression so that there are no negative exponents.

A. ( )02xy B. ( )32x C. 22yx

D. ( ) 11abc−− E. 2 4 2

3 2

a b cab c

−

F. 42

3

ab

−−

G. 34

2

mn−

H. 1 0 2

2 1 3

m n pm n p

−

− I. ( ) 23mnp

−

J. 3 2

3 2 1

d e fd e f− − −

K. 3 2 4d d d−< < L. 3 2

7 4

e ee e−

<

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations

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Hart Interactive – Algebra 1 M1 Lesson 6A ALGEBRA I

3. Determine what integer can be placed in the blank to make the statement true.

A. 43 2 12

3 ____a b ab b− = B. ( )

_____234 24

ba ba

−− =

C. 2

2 3____ 3

aa ba b

−−= D. ( )

303 5____ ____

aa ba b

=

4. Four Number Game: Use the numbers 1, 2, 3 and 4 no more than once for each problem. You may use any operations including powers and parentheses. You may NOT create a 2-digit number (1 & 2 ≠ 12). For example, if the number was 10, then we could do any of the following: 1 + 2 + 3 + 4 = 10 or 2 • 3 + 4 = 10 or 32 + 1 = 10.

A. The number is 12: _____________________________________________________________________ B. The number is 15: _____________________________________________________________________ C. The number is 25: _____________________________________________________________________ D. The number is 32: _____________________________________________________________________

Lesson 6A: Algebraic Expressions—Exponent Rules & Order of Operations

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This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M1-TE-1.3.0-07.2015

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.