First step: combine 2^2z into (2^2)^z = 4^z by the power rule

4^z times 3^z = 1/144

This is so that we obtain the same power required to use the next rule, the same power rule of indices. We multiply the base to become

(4 x 3)^z = 1/144
12^z = 1/144

Note that 144 is 12^2, so

12^z = 1/(12^2)

But as we know it, 1/(12^2) = 12^-2 since 1/a^n = a^(-n)

12^z = 12^-2

This can only equal each other when the powers are the same,

z = -2.

It’s coincidental that I have the same name Eric as your teacher or your tutor. I hope your teacher/tutor has explained the concepts well.

Not a coincidence. He was specifically asking for you to help him lol

Yeah not a coincidence. I am straight away skipped this question without think twice when i saw Eric in comments. :)