Rules of Exponents
There are many rules that apply to operations involving exponents. In this question, we'll need the following:
The division rule
- ⇒ [tex]\dfrac{a^n}{a^m}=a^{n-m}[/tex]
Solving the Question
We're given:
[tex]z^{21}\div z^7=z^k[/tex] (solve for k.)
⇒ Rewrite as a fraction:
[tex]\dfrac{z^{21}}{z^7}=z^k[/tex]
⇒ Use the division rule:
[tex]z^{21-7}=z^k\\z^{14}=z^k\\14=k[/tex]
Therefore, the value of k is 14.
Answer
k = 14
