Thank you for the opportunity to help you with your question! Hope your day is going well!

This is a law of exponents problem. When we are multiplying by the same base (i.e. z) in this case, we simply can add the exponents to simplify the problem.

z^3 * z^9 x z^5

z^(3+9+5)

z^17.

You can always do an example problem to ensure that you are right. Let's make 2 our base.

2^3 * 2^9 * z^5= 131, 072

Use the law of exponents simplified equation

2^17=131,072.

Check! They are the exact same answer.

Please let me know if you need any clarification. I'm always happy to answer your questions.