Power Value Zero and Negative Exponents

_________________________ Zero exponent: Examples:

_______________________ Negative exponent: Think: Examples:

Simplify (-5) One cup is 2 -4 gallons. What does this mean in simplified terms?

Try it! Simplify (-2) -4 (-2) A sand fly may have a wingspan up to 5 -3 m. What does this mean in simplified terms?

Multiplication of Exponents Recall: 4 3 (exponential notation) (expanded form) (simplified form)

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

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

Examples: 5 3 ∙ 5 2 (-2)(-2) 4 *NO exponent implies a power of 1 x 2 ∙ x 3 ∙ x 4

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

-3 3 (-3) (-3) 2

POWER OF A POWER (3 2 ) ∙ 3 2 ∙ 3 2 (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. (x a ) b = x a∙b

For example: (x 3 ) 4 (x 2 ) 5

Try these on your own… (3 3 ) 2 (p 4 ) 4 (n 4 ) 5 [(-3) 5 ] 2

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

Try these on your own… (st) 2 (4yz) 3 (-2x 4 y 7 z 9 ) 5 (-x 2 y 8 ) 3

REVIEW Product of Powers (ADD the exponents) x a ∙x b = x a+b Power of a Power (MULTIPLY the exponents) (x a ) b = x a∙b Power of a Product (“DISTRIBUTE” the exponents) (xy) a = x a y a

Now put it all together! (3b) 3 b-4x (x 3 ) 2 2x 3 (-3x) 2 4x (-x x 3 ) 2 (abc 2 ) 3 ab(5y 2 ) 3 (y 3 ) 2

Division Properties of Exponents The Quotient of Powers To divide powers that have the same base, you _____________________________ Ex:

Simplify the following.

Power of a Quotient

Simplify the following.

Try It!

Using more than one property… a) b)

Give it a try:

Challenge:

Review Anything raised to a zero power is… When you have a negative exponent…

Try It!

Points to remember…

Warm Up