Final answer:
The properties used in Steps 1 and 3 are the commutative property and the distributive property, respectively.
Explanation:
In Step 1, the commutative property facilitated reordering terms within the parentheses, interchanging '11z' and '6z'. This property allows altering the order of addition or multiplication without changing the result. In Step 3, the distributive property was applied, where '5' was multiplied across all terms within the parentheses, resulting in '5(17z + 29)'. The distributive property states that multiplying a number by a group of numbers inside parentheses or brackets yields the product of that number with each term inside. These properties, integral in simplifying expressions, enable strategic rearrangements and product distributions to attain the final simplified form.