"
" .
________________________________
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: → ![1000^m=(10^3)^m = 10^(^3^*^m)=10^(^3^m^) .](/tpl/images/0557/0747/5905c.png)
________
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:
________
→
; ![a\neq 0 .](/tpl/images/0557/0747/04a29.png)
________
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!
_______________________________________