Properties of operations with rational numbers

General Information
"Generalise the properties of operations with rational numbers, including the properties of exponents." is a bullet point under Patterns and Relationships, Number and Algebra of Level 6 Mathematics and Statistics. Although not specifically assessed, these properties are to be understood for the successful simplification/solving of most equations.

What you need to know
Distributive Property: ax+ay=a(x+y)

Associative Properties: a+b+c=(a+b)+c=a+(b+c)   ab(c)=a(bc)

Commutative Properties: a+b=b+a   ab=ba

Properties of exponents: axy+bxy=(a+b)xy   xaxb=xa+b    xa/xb=xa-b(xa)b=xab(x/y)a=xa/ya