If $10^{x} \cdot 10^{5}=100^{4}$, what is the value of $x$ ?
(A) 1
(B) 35
(C) 11
(D) $\frac{4}{5}$
(E) 3
Since $100=10^{2}$, then $100^{4}=\left(10^{2}\right)^{4}=10^{8}$.

Therefore, we must solve the equation $10^{x} \cdot 10^{5}=10^{8}$, which is equivalent to $10^{x+5}=10^{8}$.

Thus, $x+5=8$ or $x=3$.

ANSWER: (E)