$$z^{6x^{3}} / z^{4x^{5}}$$
In power towers like these, always solve from the "deepest level" first, in the notation, the highest level.
$$z^{216x^{3}} / z^{1024x^{5}}$$
Remember the formula:
ab / ac = ab - c
We get:
$$z^{216x^{3}-1024x^{5}} = z^{x^{3}(216-1024x^{2})}= z^{8x^{3}(27-128x^{2})}$$
Did you want it expressed in some other way?
$$\\\dfrac{z^6x^3}{z^4x^5}\\\\\\
=\dfrac{z^{6-4}}{x^{5-3}}\\\\\\
=\dfrac{z^{2}}{x^{2}}\\\\\\$$
Yeah, the more experienced math helper and friend Melody, and me, interpreted the question differently.
At any rate, please include paranthesis and/or multiplication symbols to make the question unambiguous. :)
Tetration and I have interpreted your question differently. To tell you the truth either of us interpreted it as it tecnically should have been interpreted.
Technically this is correct.
z^6x^3/z^4x^5
$$\\z^6\times \dfrac{x^3}{z^4}\times x^5\\\\\\
=\dfrac{z^6*x^3*x^5}{z^4}\\\\\\
=\dfrac{z^2*x^8}{1}\\\\\\
=z^2*x^8\\\\
=z^2x^8$$