Download 10 Rules of Exponents

Common Tools Used in Algebra
Information Sheet 1-1
Acronym
a = p% • b
|a|
a:b
AI
AIO
APA
APM
CLT
CON
CPA
CPM
CST
CVC
DP
D2 P
EVN
EXEQ
Fraction Tools
AF
DF
MF
SF
Name
Percent Equation: “a is ‘p’ percent of b”
Absolute Value
Ratio Tool
Additive Inverse
Addition Identity of Zero
Associative Property of Addition
Associative Property of Multiplication
Combining Like Terms
Category of Numbers
Commutative Property of Addition
Commutative Property of Multiplication
Conflicting Sign Tool
Coefficient, Variable, Constant
Distributive Property
Decimal to Percent Conversion
Exponent, Variables, Numbers
Expression Equation
f(x)
Function Tool: “f of x”
GR
Golden Rule of Equations
(GS)EMA = Ans
DS
L
R
Inequalities Tools
<
>
≤
≥
kPAV Tool
P(o) • sf = P(d)
A(o) • sf 2 = A(d)
V(o) • sf 3 = V(d)
MI
MI1
MP0
MP(–1)
P(A)
PPR
PTFG
RCcola
Order of Operations Tool
Adding Fractions
Dividing Fractions
Multiplying Fractions
Subtracting Fractions
Example
50 = p% of 100
| –3 | = 3
 = 3:4
3 + (–3) = 0
x+0=x
(3 + 4) + 5 = 3+ (4 + 5)
(3 • 4) • 5 = 3 • (4 • 5)
x4 + 2x4= 3x4
N, Z, Q, R, C
3+4= 4+3
3•4= 4•3
+(– 3) = –3
2x + 7
2,x,7
3(2x+4) = 6x+12
.01 = 1%
x4 , x , 3
5x + 6
(expression)
5x + 6 = 36 (equation)
+ = +=
÷ = •=
•=
– = – =
Less than
Greater than
Less than OR equal to
Greater than OR equal to
f(x) = 2x
when x= 3
f(3) = 2(3)  f(3) = 6
x=x
x+–•÷5=x+–•÷ 5
Grouping Symbols:(), [], {}
Exponents: x4
Multiplication & Division
Addition & Subtraction
x<5
○
x>5 ○
x≤ 5
x≥ 5
Perimeter of original •Scale Factor = Perimeter
Area of original •Scale Factor 2 =Area of dilated
Volume of original • Scale Factor 3 = Volume
Multiplication Inverse
Multiplication Identity of One
Multiplication Property of Zero
Multiplication Property of Negative One
Probability Tool
Product Property of Radicals
Pattern, Table, Function, Graph
Matrix Tool “n x m” Rows then Columns
(k=2) 4cm • 2 = 8 cm
(k=2) 4cm2 • 22 = 16 cm2
(k=2) 4cm3 • 23 = 32 cm3
5• =1
1•x=x
0•x=0
x • (–1) = – x
P(A)= 
 = √x • √y
1,2,3,4,5,…
“3x4” “3 by 4” dimensions
3 rows 4 columns
Ratio and Proportion Tools
kRAP
Constant of Proportionality RAP
MEP
UR RAP
RT
Sub
TIB
V-MM
VLNR
VRNL
_
X= Σ/n
ZPP
4-4 Slope Tool
(3) 3 cats 9 cats
(3) 4 dogs = x dogs
Means Extremes Property (Cross Product Property) 3 cats 9 cats
4 dogs = x dogs
3:4 = 9:x → 3x=4•9
Unit Rate RAP
() 3 cats 4 dogs
() 9 cats = x dogs
(4) 1 cats 4 dogs
(4) 3 cats = x dogs
Reciprocal Tool (Multiplication Inverse)
x = 
()x = ()
Substitution Tool
2x + 3 where x= 4
2(4) + 3
Top in Box
=
Verbal to Mathematical Model
3 cats and 4 dogs = 3c + 4d
Variables Left Numbers Right
x=4
Variables Right Numbers Left
4=x
Averaging Tool
Zero Property Principle
4 Types of Slope
1. UR + “up right positive”
2. DR - “down right negative”
3. Zero “left to right”
4. Undefined “up and down”
4 Ways to Calculate Slope
1. y =ax + b a= slope, b= y-axis intercept
2. Rise = slope
Run
3.  y = slope
x
4. y2 – y1 = slope
x2 – x 1
10 Rules of Exponents
1. a1= a
2. an = aaaa…an
3. a0 = 1 a  0
4. a n = 1/a+n
5. ap/r = ap
6. an  am = a(n+m)
7. an = a(nm)
am
8. (a  b) n = an bn
9. (a/b) n = a n / b n
10. (a n ) m = a nm
x Bar = Sigma/number
0 = (x+2) (x–10)
Basic Power of 1 Property
Basic Power Property
Basic Power of 0 Property
Basic Negative Exponent Property
Basic Fractional Exponent Property
Product of Powers Property
Quotient of Powers Property
Power of a Product Property
Power of a Quotient Property
Power of a Power Property
y = 2x+3 Slope = +2
Rise = 3 Slope = 
Run = 8
 y = 5 Slope = 
x=8
(2, 4) (8, 9) Slope = 
y2 – y1
(9 – 4) = 
x2 – x1 = (8 – 2)
31= 3
34 = 3  3  3  3
30 = 1
3 4 = 1/34
53/4 = 4³
34  35 = 3(4+5)
34 = 3(45)
35
(3  4) 5 = 35  45
(3/4) 5 = 3 5 / 4 5
(3 4 ) 5 = 3 45
Geometry Formulas
1. P(triangle) = s + s + s
2. P(square) = 4s
3. P(rectangle) = ▪ 2(l + w)
▪ 2 l + 2w
▪ l+l+w+w
▪ s+s+s+s
4. C(circle) = ▪ πd
▪ 2πr
∏▪⁴⁵⁷⁸∏∆±² ³ ¹
º 
              √3