1. Multiplication of Exponents
Recall:
(exponential notation)
(expanded form)
(simplified form)

2. Product of Powers 22 • 23 Expanded form: Exponential notation:
What is the “rule”?
We can multiply powers only when ________________!!

3. What happens when bases are not the same??
23 • 32
We must ________________________________
Exponents _______________________________
________________________________________

4. Examples: 53 ∙ 52 (-2)(-2)4 *NO exponent implies a power of 1
x2 ∙ x3 ∙ x4

5. BE CAREFUL… These are not the same!!! -2 2 (-2)2
(-2)2
“The opposite of 22” ∙ -2
or or (22) (-2) (-2)

6. (-3)3
(-3)2

7. POWER OF A POWER (32)3 32 ∙ 32 ∙ 32 (product of a power)
3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3 (expanded form)

8. Rather than writing out a problem in an expanded form, use the “shortcut”
Rule: When given a power of a power,
______________ the exponents.
(xa)b = x a∙b

9. For example:
(x3)4
(x2)5

10. Try these on your own…
(33)2
(p4)4
(n4)5
[(-3)5]2

11. POWER OF A PRODUCT Rule: When given a power of a product, _________
_________________________________________
(xy)3
(x2y3z)5
(4∙3)2
(-3xy)4

12. Try these on your own…
(st)2
(4yz)3
(-2x4y7z9)5
(-x2y8)3

13. REVIEW Product of Powers (ADD the exponents) xa∙xb = xa+b
Power of a Power (MULTIPLY the exponents)
(xa)b = xa∙b
Power of a Product (“DISTRIBUTE” the exponents) (xy)a = xaya

14. Now put it all together!
(3b)3 • b -4x • (x3)2 2x3 • (-3x)2 4x • (-x • x3)2 (abc2)3 • ab (5y2)3 • (y3)2