For two natural numbers $a$ and $b$, the three numbers $a ^ { n } , 2 ^ { 4 } \times 3 ^ { 6 } , b ^ { n }$ form a geometric sequence in this order. Find the minimum value of $a b$. (Here, $n$ is a natural number.) [4 points]
For two natural numbers $a$ and $b$, the three numbers $a ^ { n } , 2 ^ { 4 } \times 3 ^ { 6 } , b ^ { n }$ form a geometric sequence in this order. Find the minimum value of $a b$. (Here, $n$ is a natural number.) [4 points]