Algebra Period 3

Exponents: 5-1

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!!!!
-2^5 = -32
-2^4 = -16

MULTIPLYING Powers with LIKE BASES:
Simply ADD THE POWERS
m^5m^3 = m^8
You can check this by EXPANDING:
(mmmmm)(mmm) = m^8

DIVIDING Powers with LIKE BASES:
Simply SUBTRACT the POWERS
m^8/ m^5 = m^3

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

ZERO POWERS:
Anything to the zero power = 1
(except zero to the zero power is undefined)
Proof of this was given in class:
By the transitive property of equality : 1 = m^0

NEGATIVE POWERS = FRACTIONS
They're in the wrong place in the fraction!
NEGATIVE POWERS ARE NOT NEGATIVE NUMBERS!
THEY HAPPEN WHEN THERE IS A DIVISION OF LIKE BASES WHERE THE POWER ON THE TOP IS SMALLER THAN THE POWER ON THE BOTTOM!
WHEN YOU USE THE POWER RULES, YOU WILL SUBTRACT A BIGGER NUMBER FROM A SMALLER NUMBER AND THAT WILL CREATE A NEGATIVE POWER!

EXAMPLE:
m^3/m^5 = m^-2


m^3/m^5 = m^-2
mmm/mmmmm 1/mm

Again, by transitive property of equality:
m^3/m^5 = m^-2 = 1/m^2
m2

EXPRESS NEGATIVE POWERS WITHOUT EXPONENTS:
1) MOVE TO DENOMINATOR
2) EXPAND THE POWER

EXAMPLE:
(-2)^-5 = 1/(-2)^5 = 1/-32 OR -1/32

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


More on Exponents: 5-2

POWER to another POWER

Multiply the POWERS
(m^5)^3 = m^15
to check EXPAND it out (m^5) (m^5) (m^5) = m^15

PRODUCT to a POWER
DISTRIBUTE the power to EACH FACTOR
(m^5n^4)^3 = m^15n^12

RAISING a QUOTIENT to a POWER
distribute the power to the numerator AND to the denominator