Write the following sets in the set-builder form
(i) $\{3,6,9,12\}$ 
(ii) $\left\{2,4,8,16,32\right\}$ 
(iii) $\left\{5,25,125,625\right\}$ 
(iv) $\left\{2,4,6,...\right\}$ 
(v) $\left\{1,4,9,...,100\right\}$ 

Alternatively, $\{x:x\text{ is a multiple of 3 and }x\le 12\}$

(ii) $\left\{2,4,8,16,32\right\}$
It can be seen that $2=2^1,4=2^2,8=2^3,16=2^4$, and $32=2^5$.
$\therefore \left\{2,4,8,16,32\right\}=\{x:x=2^n,nϵN$ and $1\le n\le 5\}$

(iii) $\left\{5,25,125,625\right\}$
It can be seen that $5=5^1,25=5^2,125=5^3$, and $625=5^4$.
$\therefore \left\{5,25,125,625\right\}=\{x:x=5^n,nϵN$ and  $1\le n\le 4\}$

(iv) $\left\{2,4,6,....\right\}$
It is a set of all even natural numbers.
$\therefore \left\{2,4,6,....\right\}=\left\{x:x\text{ is an even natural number}\right\}$

(v) $\left\{1,4,9,.....100\right\}$
$\therefore \left\{1,4,\mathrm{9...100}\right\}=\{x:x=n^2,nϵN$ and $1\le n\le 10\}$

Alternatively, $\{x:x\text{ is a square of natural number and }x\le 100\}$