Question

Which property was used to simplify the expression? (3z)^2 = 3^2z^2 = 9z^2

Answer 1

One of the product rules for exponents was used.
$(ab)^{c}=a^{c}b^{c}$

Or, you can consider that the definition of an exponent and the associative and commutative properties of multiplication were used.
$(3z)^{2}\\=(3z)(3z)\\=3\cdot 3\cdot z\cdot z\\=3^{2}z^{2}\\=9z^{2}$