#1**+5 **

$$z^{6x^{3}} / z^{4x^{5}}$$

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:

a^{b} / a^{c} = a^{b - 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?

Tetration
Jan 17, 2015

#2**+5 **

$$\\\dfrac{z^6x^3}{z^4x^5}\\\\\\

=\dfrac{z^{6-4}}{x^{5-3}}\\\\\\

=\dfrac{z^{2}}{x^{2}}\\\\\\$$

Melody
Jan 17, 2015

#3**+5 **

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
Jan 17, 2015

#4**+5 **

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$$

Melody
Jan 17, 2015