Answer :
[tex]:\implies\sf\:(8^9)^p=8^{18}[/tex]
[tex]\dag\bf\:(a^m)^n=a^{mn}[/tex]
[tex]:\implies\sf8^{9p}=8^{18}[/tex]
[tex]\dag\bf\:18=9\times 2[/tex]
[tex]:\implies\sf\:8^{9p}=8^{9\times 2}[/tex]
[tex]\dag\bf\:a^x=a^y\:\longrightarrow\:x=y[/tex]
[tex]:\implies\sf\:9p=9\times 2[/tex]
[tex]:\implies\boxed{\bf{\red{p=2}}}[/tex]
