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

“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

(xy)3

(x2y3z)5

(4∙3)2

(-3xy)4

Rule: When given a power of a product, _________

_________________________________________

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