1. Warm - Up
How can you add eight 8's to get the number 1,000? (only use addition!)
Write the expression for the volume of a thick crust pizza with height "a" and radius "z".

2. Exponentials
Rules Review

3. Objectives
Students will be able to add, subtract, multiply and divide values (with variables) with exponents
Including when exponents are negative and/or rational

4. Adding Variables With Exponents
When adding variables with exponents, what happens to the exponents?
Example: 𝑥 2 +3 𝑥 2
Example: 𝑥 2 + 𝑥 3
Example: 𝑥 2 + 𝑥 3 +2 𝑥 2 +4

5. Subtracting Variables With Exponents
When subtracting variables with exponents, what happens to the exponents?
Example: 𝑥 2 −3 𝑥 2
Example: 𝑥 2 − 𝑥 3
Example: 𝑥 2 − 𝑥 3 −2 𝑥 2 −4
Example: − 𝑥 2 +𝑥+2 −( 𝑥 2 +2𝑥−3)

6. Multiplying Variables With Exponents
When multiplying variables with exponents, what happens to the exponents?
Example: 𝑥 2 (3 𝑥 2 )
Example: (𝑥 2 )( 𝑥 3 )
Example: (𝑥 2 )( 𝑥 3 )(2 𝑥 2 )(4)

7. Dividing Variables With Exponents
When dividing variables with exponents, what happens to the exponents?
Example: 𝑥 2 3 𝑥 2
Example: 𝑥 2 𝑥 3
Example: 6 𝑥 2 𝑦 6 𝑧 7 3 𝑥 2 𝑦 4 𝑧
Example: 𝑥 8 𝑦 2 2𝑥 3

8. Dividing w/ Exponents (cont.)
Explanation of why anything to the zero power is one:
3 3
3 2
3 1
3 0

9. Raising Variables To A Power
When raising variables with exponents to a power what happens to the exponents?
Example: ( 𝑥 2 ) 4
Example: (2 𝑥 3 ) 3
Example: (3 𝑤 2 x 𝑦 5 𝑧 3 ) 4
Example: [(3𝑥4𝑦7𝑧12)5 (–5𝑥9𝑦3𝑧4)2]0

10. Negative Exponents
When a variable is being raised to a negative power/exponent, what happens?
Example: 𝑥 −4
Example: 𝑥 2 𝑥 −3
Example: ( 𝑥 −2 𝑦 −3 ) −2
Example: 2 𝑥 −1
Example: (3𝑥) −2

11. Rational Exponents
2 = =
( ) 5 =
(−2) 2 =

12. Closure Simplify the following expressions: 𝑥 2 +7 𝑥 2 −2
3𝑥 3 4𝑥 5
2 𝑥 6 𝑦 2 4 𝑥 2 𝑦 3
(8 𝑥 6 ) 1 3