Given the sequence:
[tex]\frac{1}{4},3,36,432[/tex]This sequence is a geometric sequence, where the first term is 1/4, and the common ratio is 12:
[tex]\begin{gathered} a_1=\frac{1}{4} \\ a_n=\frac{1}{4}\cdot12^{n-1} \end{gathered}[/tex]The ninth term is:
[tex]\begin{gathered} a_9=\frac{1}{4}\cdot12^{9-1}=\frac{1}{4}\cdot12^8 \\ \therefore a_9=107495424 \end{gathered}[/tex]