Algebra Honors ( Periods 6 & 7)

Multiplying Monomials 4-3
POWER RULES:


MULTIPLYING Powers with LIKE BASES:

Simply ADD THE POWERS

m⁵m³ = m⁸

You can check this by EXPANDING:
(mmmmm)(mmm) = m⁸



DIVIDING Powers with LIKE BASES:

Simply SUBTRACT the POWERS

m⁸/m⁵ = m³     


Again, you can check this by EXPANDING:
mmmmmmmm/mmmmm = mmm

ZERO POWERS:

Anything to the zero power = 1


(except zero to the zero power is undefined)


Proof of this was given in class:

1 = mmmmmmmm/mmmmmmmm
= m⁸/m⁸
= m⁰ (by power rules for division)
    


By the transitive property of equality : 1 = m⁰


Review the odd/even rule

IF THERE IS A NEGATIVE INSIDE PARENTHESES:

Odd number of negative signs or odd power = negative

Even number of negative signs or even power = positive


EXAMPLES:
(-2)⁵ = -32

(-2)⁴ = +16



IF THERE IS A NEGATIVE BUT NO PARENTHESES:

ALWAYS NEGATIVE!!!!

-2⁵ = -32

-2⁴ = -16

JUST REMEMBER
NEGATIVE POWERS MEANS THE NUMBERS ARE FRACTIONS


They're in the wrong place in the fraction

m³/m⁵ = m^-2
     

m³/m⁵ = mmm/ mmmmm
= 1/mm


Again, by transitive property of equality:

m³/m⁵ = m^-2 = 1/m²

Remember the rule of powers with (  )
When there is a product inside the (  ), then everything inside is to the power!

If there are no (  ), then only the variable/number right next to the power is raised to that power.

3x^-2 does not equal (3x)^-2
The first is 3/x² and the second is 1/9x²

RESTATE A FRACTION INTO A NEGATIVE POWER:

1) Restate the denominator into a power

2) Move to the numerator by turning the power negative


EXAMPLE: 
1/32
 = 1/(2)⁵ = (2)^-5