at-home lesson 7.1 exponent properties involving products

At-Home Lesson

7.1 Exponent Properties Involving Products

• NS 2.3 - Multiply, divide, and simplify rational numbers by using exponent rules.

• AF 2.1 - Simplify and evaluate expressions that include exponents.

Math Standards

Technology Standards• 5a - Advocate and practice safe, legal, and

responsible use of information and technology.

• 6b - Select and Use applications effectively and productively.

Review

X3

Exponent

Review

X3

Base

Review

X3

The exponent and the base together are called...Power.

Review

Definition of a negative exponent

a a

n=-n 1

Exponent Properties

Involving Products

Section 7.1

Review

Product of Powers Property

a a a

m + n

=m n.

To multiply powers with the same base, add their exponents.

Using the...Product of Powers Property

7 7 7

8 + 9

=8 9. Product of

powers property

Example A

7 =

17Add Exponents

Using the...Product of Powers Property

x x x

7 + 4

=7 4. Product of

powers property

Example B

x =17

Add Exponents

Using the...Product of Powers Property

y y y

-2 + (-5)

=-2 -5. Product of

powers property

Example C

y =-7

Add Exponents

= y1

7

Definition of negative exponent

ReviewPower of a Power Property

a a

m n=

m

To simplify a power of a power,multiply exponents.

)( n

Using the...Power of a Power Property

Power of apower property

Example A

=Multiply

Exponents

6 6 4

=4)( 4 4 .

6 16

Using the...Power of a Power Property

Power of apower property

Example B

=Multiply

Exponents

-0.3 =5)( 2[ ] -0.3 )( 5 2.

-0.3 )(10

Using the...Power of a Power Property

Power of apower property

Example C

=Multiply

Exponents

m m -3

=-3)( 4 4 .

m -12

= m1

12

Definition ofnegative exponents

ReviewPower of a Product Property

ab a

m

=To simplify a power of a product,

find the power of each factor and multiply.

)(m

b

m

Using the...Power of a Product Property

Power of aproduct property

Example A

=Evaluate

power

3x 3 x4

=)( 4 4

81x 4

Using the...Power of a Product Property

Power of aproduct property

Example B

Definition ofnegative exponent

-4d =)(-3

-4 )(-3

d -3.

d 3-4 )( 3=1 1

.

Continued

Using the...Power of a Product Property

Example B continued

Evaluate Power

d 3-64 )( 3=1 1

.

= -64 d 3

1Simplify

At-Home Quiz*

*Work needs to be turned in first thing tomorrow

(You may use the previous examples for help)

Quiz

x x7 4.a)

c) y 2)( -5

b)

d)

4z )(4

rs )( 9

At-Home Quizis now complete

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