Question

Rewrite the expression in the form z n z n z, start superscript, n, end superscript. Z − 1 3 z − 5 6 = z − 6 5 ​ z − 3 1 ​ ​ =start fraction, z, start superscript, start superscript, minus, start fraction, 1, divided by, 3, end fraction, end superscript, end superscript, divided by, z, start superscript, start superscript, minus, start fraction, 5, divided by, 6, end fraction, end superscript, end superscript, end fraction, equals () Stuck

Answer 1

Answer:

$2z^4$

Step-by-step explanation:

Given the expression $\frac{z^{-1}}{3} \div\frac{z^{-5}}{6}$, we are to write it in the form of $nz^n$. To do that we will simplify the given indicinal expression as shown;

$\dfrac{z^{-1}}{3} \div\dfrac{z^{-5}}{6}\\= \dfrac{z^{-1}}{3} \times\dfrac{6}{z^{-5}}\\= \dfrac{6z^{-1}}{3z^{-5}}\\ = \dfrac{2z^{-1}}{z^{-5}}$

According to indices $\dfrac{a^m}{a^n} = a^{m-n}$, the resulting equation will become;

$= \dfrac{2z^{-1}}{z^{-5}}\\= 2z^{-1-(-5)}\\= 2z^{-1+5}\\= 2z^{4}$

Hence expression in the form $nz^n \ is \ 2z^4$.