$\frac{15^{30}}{45^{15}} =$
$\text{(A) } \left(\frac{1}{3}\right)^{15}\quad \text{(B) } \left(\frac{1}{3}\right)^{2}\quad \text{(C) } 1\quad \text{(D) } 3^{15}\quad \text{(E) } 5^{15}$
First we must convert these to the same bases. We can rewrite $45^{15}$ as $15^{15} \cdot 3^{15}$ Now
$\frac{15^{30}}{15^{15} \cdot 3^{15}}$
Canceling.... 
$\frac{15^{15}}{3^{15}} \Rightarrow (\frac{15}{3})^{15} \Rightarrow 5^{15}$
$\fbox{E}$