e)
2*2²*2³*........2²⁰⁰⁸= 2¹⁺²⁺...²⁰⁰⁸= 2^2017036
1+2+3+....2008=2008*2009/2=2017036
(8⁷⁷)⁸⁶⁷¹=[(2³)⁷⁷]⁸⁶⁷¹=2^2 003 001
2*2²*2³*........2²⁰⁰⁸ > (8⁷⁷)⁸⁶⁷¹
b)
2²⁰² + 2²⁰³= 2²⁰² *(1+2)=2²⁰²*3= (2²)¹⁰¹*3= 4¹⁰¹* 3
7³⁰⁴= 7³⁰³*7=(7³)¹⁰¹*7= 343¹⁰¹*7
4¹⁰¹* 3 < 343¹⁰¹*7