Algebra (Period 1)

Chapter 1 Review

Exponential Notation

exponent ---> little number that is raised called superscript on your computer.
4³
the 4 is the base and the 3 is the exponent.
the power is how many times the repeated multiplication will occur... in this case the power is 3!!
Some terms to know:
exponentiation notation : written with an exponent (8k)⁴
expanded notation: 8k⋅ 8k⋅ 8k⋅ 8k
(10c)³ 10⋅10⋅10⋅c⋅c⋅c
standard notation: the number value
3³ = 27
(3x)³ = 27x³
but 3x³ is just 3⋅x⋅x⋅x or just the same as you started with!! 3x³
Watch your HUGS.. they are very important in life.. and in math!!
(3x)³ where x = 2
is [(3)(2)]³ or 6 ³ = 6⋅6⋅6 = 216
but 3x³ is 3 (2)³ or 3⋅2⋅2⋅2⋅ = 24

Powers of negative numbers and the odd/even rule

If there is a negative inside the (hugs)
odd number of negative signs or an odd power ---> its negative

even # of negative signs or an even power ---> positive

(-2) ⁵ really means (-2)(-2)(-2)(-2)(-2) = -32
(-2) ⁴ really means (-2)(-2)(-2)(-2) = 16

If there is a negative but NO (hugs)... it is ALWAYS negative
-2⁵ = -32 and
-2 ⁴ = -16
because these really read
"Take the opposite of 2 to the 5th power" and
"Take the opposite of 2 to the 4th power"

Equation Vocab

solution = answer

replacement set: the set of answers that you have to choose from for the answer.
solution set: all the answers that make a statement true

{ } is set symbol
For example
solve y + 4 = 10 if the replacement set is {2, 6, 10}
you discover that
6 + 4 = 10 makes the statement true so 6 is the solution set and you write it
{6}

But what if you have y + 4 = 10
but the replacement set is { 2, 7, 10}
when you plug in each of the values none of them are true
2 + 4 ≠ 10
7 + 4 ≠ 10
10 + 4 ≠ 10
so the solution set is the NULL SET. which you write
{ } or ∅

Equations can be true, false or open!!
If it is numerical they are either true or false...
If equation is Algebraic ( variables) it is always OPEN