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

• ⇒
  `(a^n)/(a^m)=a^(n-m)`

Solving the Question

We're given:

`z^(21)/ z^7=z^k` (solve for k.)

⇒ Rewrite as a fraction:

`(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