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)`