If $\left(2^{4}\right)\left(3^{6}\right)=9\left(6^{x}\right)$, what is the value of $x$ ?
(A) 2
(B) 3
(C) 4
(D) 216
(E) 8
Solution 1

The left side of the given equation equals $\left(2^{4}\right)\left(3^{6}\right)=16(729)=11664$.

Thus, $9\left(6^{x}\right)=11664$ or $6^{x}=1296$.

Since $6^{4}=1296$, then $x=4$.

Solution 2

Rearranging the left side, $\left(2^{4}\right)\left(3^{6}\right)=\left(2^{4}\right)\left(3^{4}\right)\left(3^{2}\right)=(2 \times 3)^{4}\left(3^{2}\right)=6^{4}(9)=9\left(6^{4}\right)$.

Comparing with $9\left(6^{x}\right)$, we see that $x=4$.

ANswer: (C)