Answer:
[tex]\huge\boxed{p=2}[/tex]
Step-by-step explanation:
In order to simplify this equation [tex](8^9)^p = 8^{18}[/tex], we have to use basic exponent rules.
Exponent rules tell us that [tex](a^b)^c = a^{b\cdot c}[/tex].
We have [tex](8^9)^p[/tex], so this means that it's equivalent to [tex]8^{9 \cdot p}[/tex] or just [tex]8^{9p}[/tex].
Now, we have [tex]8^{9p}=8^{18}[/tex]
Let's just focus on the exponents for now.
Since we know that in order for [tex]8^{9p}[/tex] to be equivalent to [tex]8^{18}[/tex], the exponents must be the exact same. So, [tex]9p=18[/tex].
We can find p by divide both sides by 9.
[tex]p = 2[/tex]
Hope this helped!
