The basic properties

The commutative property:

a + b = b + a        Commutative property of addition

a · b = b · a          Commutative property of multiplication

The associative property:

a + (b + c) = (a + b) + c       Associative property of addition

a(b · c) = (a · b)c                  Associative property of multiplication

a(b + c – d) =  a · b + a · c – a · d                Distributing multiplication over  addition and                                                                               subtraction


The numbers 0 and 1 have special roles in algebra — as identities.

a + 0 = 0 + a = a      Adding 0 to a number doesn’t change that number; the number keeps                                    its identity.

a · 1 = 1 · a = a       Multiplying a number by 1 doesn’t change that number; the number                                       keeps its identity.


A number and its additive inverse add up to 0 :                                9 + (–9) = 0

A number and its multiplicative inverse have a product of 1:        7.  (1/7) = 1


Any number raised to the power of “one” equals itself. One raised to any power is one.

Product Rule:  when multiplying two powers that have the same base, you can add the exponents.

Power Rule: to raise a power to a power, just multiply the exponents. 

Quotient Rule:  we can divide two powers with the same base by subtracting the exponents.

Any nonzero number raised to the power of zero equals 1:

Negative Exponents: any nonzero number raised to a negative power equals its reciprocal raised to the opposite positive power: