Find the Power Series for the Function $f ( x ) = e ^ { x ^ { 8 } }$

Multiple Choice

Find the power series for the function $f ( x ) = e ^ { x ^ { 8 } }$ using the power series for $e ^ { x }$ .

A) $\sum _ { n = 1 } ^ { \infty } \frac { x ^ { 8 ( n + 1 ) } } { ( n + 1 ) ! }$
B) $\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 8 n } } { n ! }$
C) $\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 8 ( n + 1 ) } } { ( n + 1 ) ! }$
D) $\sum _ { n = 0 } ^ { \infty } \frac { x ^ { 8 n } } { ( n + 1 ) ! }$
E) $\sum _ { n = 1 } ^ { \infty } \frac { x ^ { 8 ( n + 1 ) } } { n ! }$