" " .
________________________________
Step-by-step explanation:
________________________________
The question states: "Can [you] help [me] find out what "c" is ? " .
________
"Can [you] help [me] find out what "c" is ? " .
→ We are to "Part C" —within the "attached image" given:
________
→ " ÷ " ; can be written in the form of: " " .
→ Express z in terms of m and n .
________
Note: Rewrite: " " ; and: " " ; as powers of "" ;
→ with "" being the "base number" .
________
Let us start with: " " .
Note that the number: " " ;
→ since " " ; has 3 (three) zeros after the "1" digit;
→ & since: " " .
So: → .
Now, let's simplify further.
Note the "multiplication property" of exponents:
→ .
As such: →
________
Likewise: We can continue by rewriting our other term:
→ " " ; as a power of "" ;
with "" being the "base number."
Note that the number: " " ;
→ since " " ; has 2 (two) zeros after the "1" digit;
→ & since: " " .
So:
→ .
Now, let's simplify further.
________
Again: As aforementioned:
Note the "multiplication property" of exponents:
→ .
As such:
→ .
________
Now, refer to the original problem:
→ " ÷ " ;
Rewrite this expression by substituting:
→ " " ; ← [for: " ."] ; And:
→ " " ; ← [for: " ."] ;
As follows:
→ " ÷ " .
________
Now: Note the following "division property" of exponents:
________
→ ;
________
As such; let's rewrite our expression; and simplify—by plugging in our values into the "equation/formula" directly above; in which:
________
→ " " [in the aforementioned formula] is: " " .
→ " " [the 'exponent' in the aforementioned formula] is:
" " .
→ " " [the 'exponent' in the aforementioned formula is:
" " .
→ " " [in the aforementioned formula] is: " " ;
→ " " [in the aforementioned formula] is: " " .
________
→ Let's plug in our values; and then "simplify" ; as follows:
________
→ ? ;
.
→ .
________
So: → " " ;
↔ " " .
→ " " .
_______________________________________
Hope this answer is helpful.
Best wishes to you in your academic endeavors
—and within the "" community!
_______________________________________