1. 7.1 Zero and Negative Exponents:
Base: A number that is multiplied repeatedly.
Exponent: A number that shows repeated multiplication.
Property: A character or attribute that something has.

2. GOAL:

3. An exponent equation has two components:
Definition:
An exponent equation has two components:
𝑏 𝑥
Exponent
Base

4. 𝑎 0 = 1 For every number a, Ex: 40 = 1 (-3)0 = 1 1000 = 1
ZERO: as an exponent
PROPERTIES:
For every number a,
𝑎 0 = 1
Ex:
40 = 1
(-3)0 = 1
1000 = 1
1,000,0000 = 1
(-½) 0 = 1

5. Simplify the following exponents:
YOU TRY IT:
Simplify the following exponents:
-1 0
(-1) 0
m 0
-1/3 0

6. -1 0 = -1 (-1) 0 = 1 m 0 = 1 -1/3 0 = -1 SOLUTION:
No matter what integer it is, anything to the power of zero is 1.
-1 0 = -1
(-1) 0 = 1
m 0 = 1
-1/3 0 = -1

7. 𝑎 −𝑛 = 1 𝑎 𝑛 For every nonzero number a and integer n
Negative numbers: as an exponents
PROPERTIES:
For every nonzero
number a and integer n
𝑎 −𝑛 = 1 𝑎 𝑛

8. NOTE:
In math we never like to work with negative exponents.
We must always provide answers with positive exponents.
Ex: 
 1 9
3 −2
 −
 − 1 4
−2 −2

9. 1 3 −2 1( 3 +2 ) 1(9) = 9 6 2 −2 6( 2 +2 ) 6(4) =24 Ex:
ALSO:
If negative exponents are in the denominator, we still turn them into positive.
Ex:
1 3 −2
1( 3 +2 )
1(9) = 9
6 2 −2
6( 2 +2 )
6(4) =24

10. b) 1 𝑥 −5 a)5a3b-2 d) 𝑛 −2 𝑚 −5 c)4c-3r
SIMPLIFYING EXPONENTIAL EXPRESSIONS:
Once again, always give answers with positive exponents only!
Ex: What is the simplified form of
each expression?
b) 1 𝑥 −5
a)5a3b-2
d) 𝑛 −2 𝑚 −5
c)4c-3r

11.  5𝑎3 𝑏 2 a)5a3b-2 b) 1 𝑥 −5  x5  4𝑟 𝑐 3 c) 4c-3r d) 𝑛 −2 𝑚 −5
SOLUTIONS:
Switch the integers that have negative to the other side.
 5𝑎3 𝑏 2
a)5a3b-2
b) 1 𝑥 −5
 x5
 4𝑟 𝑐 3
c) 4c-3r
d) 𝑛 −2 𝑚 −5
 𝑚5 𝑛 2

12. VIDEO: Get a hot chocolate and enjoy this!!!. Exponents Definition
Negative Exponents
Negative and Positive Exponents

13. CLASSWORK: Page :
Problems: As many as needed to understand the concept