Warm UpI can simplify expressions with exponents.

1.What is the value of 3x3+2 when x=10?

2.You put $500 in an account that doubles every year.a.What is the equation for this

situation?

b.How much money would you have after 4 years?

𝟑𝟎𝟎𝟐

(x=years y=money)

𝒚=𝟓𝟎𝟎(𝟐)𝟒=$𝟖𝟎𝟎𝟎

Homework Questions

What an Exponent Represents

An exponent tells how many times a number is multiplied by itself.

34= 3 3 3 3= 81

How do you say this?

three to the third power

or

three cubed

3 3Base

Exponent

three to the 2nd power

Or

three squared

3 2Base

Exponent

How do you say this?

2. 8 8 8 8 =

Practice: Write in many different ways

1. 9 9 =

3. x x x x x =

4096

eight

x

Exponent Rules

𝑥𝑚 ∙ 𝑥𝑛=¿

Part 1

Product Rule:

𝒙𝒎+𝒏

Multiply same base, add the exponents

𝑥5 ∙𝑥3=𝑥8Example:

𝒙𝒎

𝒙𝒏 =¿

Part 2

Quotient Rule:

𝒙𝒎−𝒏

Divide same base, subtract the exponents

𝑥11

𝑥3 =𝑥8Example:

(𝒙 ¿¿𝒎)𝒏=¿ ¿

Part 3

Power Rule:

𝒙𝒎 ∙𝒏

Same base, multiply the exponents

(𝑥¿¿4 )2=𝑥8 ¿Example:

(𝒙𝒚 )𝒏=¿

Part 4

Expanded Power Rule:

(𝒙)𝒏¿

Apply outside exponent to all parts inside parenthesis

(3 𝑥¿¿ 4)2=32(𝑥4)2¿Example:

¿9 𝑥8

=

Part 5

Expanded Power Rule (cont):

( 𝑥2

𝑦 )4

=¿Example:

( 𝒙𝒏

𝒚𝒏 )Apply outside exponent to all

parts inside parenthesis

( 𝑥8

𝑦 4 )

(𝒙)𝟎=¿

Part 6

Zero Exponent Rule:

𝟏

Any base raised to 0 equals 1.

Example: 𝟏

NOTES

Negative ExponentsNegative exponents tell you how many times

you should divide by a number

Negative exponents move the base to bottom of a fraction

Note: the exponent becomes positive

Negative Exponents

25

1

5

12

Partners

Find a partner with a different letter

Compare and check each others answers

Worksheet

Complete any 10 problems

What’s the difference?

1)

2)

What’s the difference?

3)

4)