Answer:
p=-24
Step-by-step explanation:
The given expression is:
[tex](\frac{1}{6})^p=36^3\times6^{18}[/tex]
We express everything to base 6.
[tex](6)^{-p}=6^{2\times3}\times6^{18}[/tex]
[tex](6)^{-p}=6^{6}\times6^{18}[/tex]
Use the product rule: [tex]a^m\timesa^n=a^{m+n}[/tex]
[tex](6)^{-p}=6^{6+18}[/tex]
[tex](6)^{-p}=6^{24}[/tex]
The bases are the same so we equate the exponents.
[tex]-p=24[/tex]
p=-24
