Which of the following is the largest?

Let's simplify each option to comparable base powers:
A) 2²⁷ already in base 2
B) 125³ = (5³)³ = 5⁹
C) 5¹⁸ already in base 5
D) 4⁴ × 1024=(2²)⁴× 2¹⁰ = 2⁸× 2¹⁰ = 2¹⁸
E) 27⁹ = (3³)⁹ = 3²⁷

Now observe:
5¹⁸ is clearly much larger than 5⁹
2²⁷ is larger than 2¹⁸

But base 3 raised to 27 (i.e, 3²⁷) grows faster than all

Since 3²⁷ increases faster than any of the others, option E is the largest.