How many different dna strands composed of 100 nucleotides could possibly exist?

There are 4¹⁰⁰ possible strands, approximately 1.61x10⁶⁰

Explanation:

This is a combinatorics problem. Each nucleotide has the possibility of being one of the four common nucleotides, adenine (A), guanine (G), thymine (T) and cytosine (C).

If the strand would be 1 nucleotide long, the possibilities would be 4, one for each possible nucleotide. If the strand would be 2 nucleotides long, for each nucleotide on the first position there would be four possible nucleotides on the second position, giving 4x4=4²=16 possible strands.

For 3 nucleotides long you have 4 possible nucleotides for each of the 2-nucleotide-long strands, 4x4x4=4²=64 possible strands. Following that pattern, for a 100 nucleotide long DNA strand, there would be 4x4x...x4x4=4¹⁰⁰ possible strands.