For this case we must indicate expressions equivalent to:
[tex]\frac {36 ^ x} {6 ^ x}[/tex]
We have to:
[tex]36 ^ x = (6 ^ 2) ^ x = 6 ^ {2x}[/tex]
Rewriting the expression:
[tex]\frac {6 ^ {2x}} {6 ^ x}[/tex]
To divide powers of the same base, we place the same base and subtract the exponents:
[tex]6 ^ {2x-x} = 6 ^ x[/tex]
The options are:
A) [tex]\frac {6 ^ {x} * 6 ^{ x}} {6^{x}}[/tex]
B) 6
C) [tex](\frac {36} {6}) ^ x[/tex]
D) [tex](36-6) ^ x[/tex]
E) [tex]6 ^ x[/tex]
F) [tex]36 ^ x[/tex]
So if we simplify option A) we have: [tex]6 ^ x[/tex]
Option C) we have: [tex]6 ^ x[/tex]
Option E) is [tex]6 ^ x[/tex]
Answer:
Option A, C, E
