1/16x4^3x4^x = 4^6

Let's solve the equation step by step:

Starting with the equation:

\[
\frac{1}{16} \times 4^3 \times 4^x = 4^6
\]

First, we can express \( 16 \) as a power of \( 4 \):
\[
16 = 4^2
\]

Thus,

\[
\frac{1}{16} = \frac{1}{4^2} = 4^{-2}
\]

Now, substituting this into the equation gives:

\[
4^{-2} \times 4^3 \times 4^x = 4^6
\]

Using the properties of exponents, we can combine the left side:

\[
4^{-2 + 3 + x} = 4^{1 + x}
\]

Setting both sides equal to each other, we have:

\[
4^{1 + x} = 4^6
\]

Since the bases are the same, we can equate the exponents:

\[
1 + x = 6
\]

Now, solving for \( x \):

\[
x = 6 - 1 = 5
\]

Thus, the solution is:

\[
\boxed{5}
\]