[(z^n)^3] / [z^n*z^3]

How can I set this up? I'm pretty sure you have to simplify so that it's z^3n / z^n+3 but where can I do from there? or am I messing up a step somewhere?

(z^n)^3= z^3n
and
z^n * Z^3= Z^(n+3)

so z^3n / Z^(n+3) = z^(3n-n+3)

To simplify the expression, you correctly simplified (z^n)^3 as z^3n and z^n * z^3 as z^(n+3).

Now, to divide z^3n by z^(n+3), you can subtract the exponents since they have the same base z.

So, z^3n / z^(n+3) can be simplified as z^(3n - (n+3)).

Simplifying the exponent, we have 3n - (n+3) = 3n - n - 3 = 2n - 3.

Therefore, the simplified expression is z^(2n - 3).

You correctly simplified the expression by subtracting the exponents of z. Well done!