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Math 1030-004
Algebra Review
Fall 2009
Order of Arithmetic Operations
Rules for Exponents
1.
Parentheses
1.
x a ⋅ x b = x a +b
2.
Exponents
2.
(x )
3.
Multiplication/Division
3.
x0 = 1
4.
x−a =
5.
( xy ) a = x a y a
6.
x
xa
 y  = xb
 
4.
Addition/Subtraction
Properties of Algebra
1.
a+b=b+a
a b
= x ab
1
xa
a
2.
(a + b) + c = a + (b + c)
3.
a(b + c) = ab + ac
4.
ab = ba
Rules for Negative Numbers
5.
(ab)c = a (bc)
1.
a + ( −b ) = a − b
6.
1
a  =1
a
2.
a − ( −b ) = a + b
3.
(−a)b = a(−b) = − ab
4.
(−a)( −b) = ab
5.
−( − a ) = a
7.
a + (−a ) = 0
8.
1a = a
9.
0a = 0
Common Mistakes
1.
xa ≠ x ⋅ a
2.
− x 2 ≠ (− x)2