**Exponents**

### 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

### Identities

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.

### Inverses

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: **