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: