
For #1 I meant to put (a4)(a4)

Sorry I meant (a4)(a+4)

#3, I see a common factor
3ab(a + 2 + 3b)
#4, (2r+1)(r+1)
#5 common factor
z(z^2 + 6z + 9), now I see a perfect square
= z(z+3)^2


1. a^216b
Answer: (a16)(a+16)
Yes !!!
2. m^2+8m+16
Answer: (m+8)^2
8 times 8 is 64, not 16
4 times 4 is 16
3. 3a^2b+6ab+9ab^2
Answer: Prime
3ab (a + 2 + 3b)
4. 2r^2+3r+1
Answer: Prime
(2r+1)(r+1)
5. z3+6z^2+9z
Answer: Prime
z (z^2 + 6 z + 9)
z (z+3)(z+3)

neither of your corrections for #1 gives you back the original result if expanded.
a^216b does not factor, unless you meant
a^216b^2, then it would be (a+4b)(a4b)

I did not see that b there !