Answer:
[tex]2z^4[/tex]
Step-by-step explanation:
Given the expression [tex]\frac{z^{-1}}{3} \div\frac{z^{-5}}{6}[/tex], we are to write it in the form of [tex]nz^n[/tex]. To do that we will simplify the given indicinal expression as shown;
[tex]\dfrac{z^{-1}}{3} \div\dfrac{z^{-5}}{6}\\= \dfrac{z^{-1}}{3} \times\dfrac{6}{z^{-5}}\\= \dfrac{6z^{-1}}{3z^{-5}}\\ = \dfrac{2z^{-1}}{z^{-5}}\\[/tex]
According to indices [tex]\dfrac{a^m}{a^n} = a^{m-n}[/tex], the resulting equation will become;
[tex]= \dfrac{2z^{-1}}{z^{-5}}\\= 2z^{-1-(-5)}\\= 2z^{-1+5}\\= 2z^{4}[/tex]
Hence expression in the form [tex]nz^n \ is \ 2z^4[/tex].
