Where's One?

Algebra Level 1

\[\large \frac{\color{brown}8^{\color{blue}p}+\color{brown}{27}^{\color{blue}p}}{\color{green}{12}^{\color{blue}p}+\color{green}{18}^{\color{blue}p}}=\frac{\color{brown}{8}+\color{brown}{27}}{\color{green}{12} + \color{green}{18}}\]

A number \(p\) satisfy the above equation. Which of these choices satisfy the value of \(p\)?