Algebra Period 3 (Review)

REVIEW:
EXPONENTS SECTIONS 5-1 TO 5-3
SCIENTIFIC NOTATION SECTION 5-4

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

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
cancel out


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 = m^8-8 = m⁰
(by power rules for division)
By the transitive property of equality : 1 = m⁰

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:
m³ / m⁵ = m^-2
m³ / m⁵ = mmm/mmmmm = 1/mm
Again, by transitive property of equality:
m³ / m⁵ = m^-2 = 1/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 with Exponents 5-2 &
Multiplying and Dividing Monomials 5-3
A monomial is an expression that is either a numeral, a variable, or a product of numerals and variables with whole number exponents.
POWER TO ANOTHER POWER
MULTIPLY the POWERS
(m⁵)³ = m¹⁵
To check, EXPAND it out:
(m⁵)(m⁵)(m⁵) = m¹⁵

PRODUCT TO A POWER
DISTRIBUTE the power to EACH FACTOR
(m⁵n⁴)³ = m¹⁵n¹²

RAISING A QUOTIENT TO A POWER:
DISTRIBUTE THE POWER to the numerator and the denominator
(m²/n⁶)³ = (m²)³/(n⁶)³ = m⁶/n¹⁸




Scientific Notation 5-4
You've had this since 6th grade!
You restate very big or very small numbers using powers of 10 in exponential form
Move the decimal so the number fits in this range: less than 10 and greater than or equal to 1 That is, 1 ≤ n < 10
Count the number of places you moved the decimal and make that your exponent
Very big numbers - exponent is positive
Very small numbers (decimals) - exponent is negative (just like a fraction!)

Remember that STANDARD notation is what you expect (the normal number)

When you multiply or divide scientific notations, use the power rules!
Just be careful that is your answer does not fit the scientific notation range, that you restate it.

TRY THIS LINK THAT TAKES YOU FROM HUGE POWERS TO
LITTLE TINY POWERS (NEGATIVE POWERS OR DECIMALS)

Try this link to practice scientific notation!

Try this link to practice multiplication of scientific notation!

Try this link to practice division!

Try this link to practice harder problems!