Distinct powers

Consider all integer combinations of \( a^b \) for \( 2 ≤ a ≤ 5 \) and \( 2 ≤ b ≤ 5 \):

\[ \begin{align} &2^2=4, 2^3=8, 2^4=16, 2^5=32\\ &3^2=9, 3^3=27, 3^4=81, 3^5=243\\ &4^2=16, 4^3=64, 4^4=256, 4^5=1024\\ &5^2=25, 5^3=125, 5^4=625, 5^5=3125\\ \end{align} \]

If they are then placed in numerical order, with any repeats removed, we get the following sequence of \( 15 \) distinct terms:

\[ 4, 8, 9, 16, 25, 27, 32, 64, 81, 125, 243, 256, 625, 1024, 3125 \]

How many distinct terms are in the sequence generated by \( a^b \) for \( 2 ≤ a ≤ 100 \) and \( 2 ≤ b ≤ 100 \)?