Answer: p = 5
Step-by-step explanation:
[tex]5^{p-3}\cdot3^{2p-8}=225\\\\5^{p-3}\cdot3^{2p-8}=15^2\\\\5^{p-3}\cdot3^{2p-8}=5^2\cdot 3^2\\\\5^{p-3}=5^2\quad and\quad 3^{2p-8}=3^2\\\\p-3=2\quad and\quad 2p-8=2\\p=5\qquad and \qquad 2p=10\rightarrow p=5[/tex]
