1. Exponents
8/14/2017

2. Exponents 𝑏𝑎𝑠𝑒 𝑒𝑥𝑝𝑜𝑛𝑒𝑛𝑡 The base is the repeated factor
The exponent s the number times the factor is multiplied to itself
3 2
2 4

3. Product rule for Exponents
If m and n are positive integers and a is a real number, the 𝑎 𝑚 ∙ 𝑎 𝑛 = 𝑎 𝑚+𝑛
4 2 ∙ 4 4 =
𝑥 3 ∙ 𝑥 7 =
2𝑥 3 ∙ 3𝑥 2 =

4. Power Rule for Exponents
If m and n are positive integers and a is a real number, then
(𝑎 𝑚 ) 𝑛 = 𝑎 𝑚𝑛
(2 3 ) 4 =
(𝑥 2 ) 7 =

5. Power of a Product rule
If n is a positive integer and a and b is a real number, then
(𝑎𝑏) 𝑛 = 𝑎 𝑛 𝑏 𝑛
(𝑥𝑦) 2 =
(2𝑡) 3 =

6. Power of a Quotient Rule
If n is a positive integer and a and c is a real number, then
( 𝑎 𝑐 ) 𝑛 = 𝑎 𝑛 𝑐 𝑛 ,𝑐≠0
( 𝑚 𝑛 ) 7 =
( 2 3 ) 2 =

7. Quotient Rule for Exponents
If m and n are integers and a is a real number, then
𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚−𝑛
𝑥 5 𝑥 3 =
𝑦 2 𝑦 8 =

8. Zero Exponent
𝑎 0 =1 as long as a does not equal 0
∞ 0 =

9. Practice in your notebook