Find the binomial expansion of \(( 1 + 6 x ) ^ { \frac { 2 } { 3 } }\) up to and including the term in \(x ^ { 2 }\).
(2 marks)
Find the binomial expansion of \(( 8 + 6 x ) ^ { \frac { 2 } { 3 } }\) up to and including the term in \(x ^ { 2 }\).
(3 marks)
Use your answer from part (b) to find an estimate for \(\sqrt [ 3 ] { 100 }\) in the form \(\frac { a } { b }\), where \(a\) and \(b\) are integers.
(2 marks)