Today’s Today’s Objective:Objective:

SWBAT SWBAT multiply multiply

and divide and divide powers.powers.

MultiplicatioMultiplication:n:

101022∙10∙1033

=?=?

3366∙3∙3

55=?=?

221010

∙2∙277=?=?

Multiplication:Multiplication:

101022∙10∙1033

= 100,000= 10= 100,000= 1055

3366∙3∙3

55= 177,147= 3= 177,147= 31111

221010

∙2∙277= 131,072= 2= 131,072= 21717

Do you see any pattern?Do you see any pattern?

Product of Powers Rule:Product of Powers Rule:

bbmm∙b∙b

nn= = bb

m+nm+n

When multipying When multipying exponents, you can add exponents, you can add

the exponents ONLY if the the exponents ONLY if the bases are the SAME!bases are the SAME!

Division:Division:

101066÷÷101033

=?=?

3377÷÷33

55=?=?

221010

÷÷2277=?=?

Division:Division:

101066÷10÷1033

= 1,000= 10= 1,000= 1033

3377÷3÷355

= 9= 3= 9= 322

221010

÷2÷277= 8= 2= 8= 233

Do you see any pattern?Do you see any pattern?

Quotient of Powers Quotient of Powers Rule:Rule:

bbmm

bbnn

When multipying exponents, you can add the When multipying exponents, you can add the exponents ONLY if the bases are the SAME!exponents ONLY if the bases are the SAME!

= bm-n

ZERO Exponent:ZERO Exponent:

For every For every nonzero #:nonzero #:

aa00=1=1

NEGATIVE Exponent:NEGATIVE Exponent:

For every For every nonzero #:nonzero #:

aa-n-n= = 1_ 1_ a ann

Simplify:Simplify:

bb00dd33bb22dd

Simplify:Simplify:

bb00dd33bb22dd

bb00bb22dd33dd

Simplify:Simplify:

bb00bb22dd33dd

Simplify:Simplify:

bb00bb22dd33dd

bb22dd44

Simplify:Simplify:

bb44dd33bb-2-2dd-3-3

Simplify:Simplify:

bb44dd33bb-2-2dd-3-3

bb44bb-2-2dd-3-3dd33

Simplify:Simplify:

bb44bb-2-2dd-3-3dd33

Simplify:Simplify:

bb44bb-2-2dd-3-3dd33

bb22dd0 0

Simplify:Simplify:bb22dd00

bb22