Multiplication of Exponents Recall: 43 (exponential notation) (expanded form) (simplified form)

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

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

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

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

-33 (-3)3 -32 (-3)2

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

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

For example: (x3)4 (x2)5

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

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

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

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

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