Question

Screenshot of the question attatched. please help me

Answer 1

Rules of Exponents

There are many rules that apply to operations involving exponents. In this question, we'll need the following:

The division rule

• ⇒ $\dfrac{a^n}{a^m}=a^{n-m}$

Solving the Question

We're given:

$z^{21}\div z^7=z^k$ (solve for k.)

⇒ Rewrite as a fraction:

$\dfrac{z^{21}}{z^7}=z^k$

⇒ Use the division rule:

$z^{21-7}=z^k\\z^{14}=z^k\\14=k$

Therefore, the value of k is 14.

Answer

k = 14