8. Given that for small values of \(x\)
$$( 1 + a x ) ^ { n } \approx 1 - 24 x + 270 x ^ { 2 }$$
where \(n\) is an integer and \(n > 1\),
- show that \(n = 16\) and find the value of \(a\),
- use your value of \(a\) and a suitable value of \(x\) to estimate the value of (0.9985) \({ } ^ { 16 }\), giving your answer to 5 decimal places.