What is the value of $2^{6}+2^{6}+2^{6}+2^{6}-4^{4}$?
(a) 0
(b) 2
(c) 4
(d) $4^{2}$
(e) $4^{4}$
The correct option is (a).

We have $2^{6}+2^{6}+2^{6}+2^{6}-4^{4}=4 \times 2^{6}-4^{4}$. There are several ways to calculate this.

Solution 1: $4 \times 2^{6}-4^{4}=4 \times\left(2^{2}\right)^{3}-4^{4}=4 \times 4^{3}-4^{4}=4^{4}-4^{4}=0$.

Solution 2: $4 \times 2^{6}-4^{4}=4\left(2^{6}-4^{3}\right)=4\left[2^{6}-\left(2^{2}\right)^{3}\right]=4\left[2^{6}-2^{6}\right]=0$.

Solution 3: $4 \times 2^{6}-4^{4}=2^{2} \times 2^{6}-\left(2^{2}\right)^{4}=2^{8}-2^{8}=0$.