If (8^x 16^(x/2)) / (2^x 4^x) = 100, find the value of x.

We know that any non-zero number raised to the power of 0 is 1, so $10^0 = 1$.
Also, $8 = 2^3$, $16 = 2^4$, and $4 = 2^2$.
Substitute these into the equation:

$$\frac{(2^3)^{\frac{x}{2}} \times (2^4)^{\frac{x}{2}}}{2^x \times (2^2)^x} = 1$$

$$\frac{2^{3 \times \frac{x}{2}} \times 2^{4 \times \frac{x}{2}}}{2^x \times 2^{2 \times x}} = 1$$ $$\frac{2^{\frac{3x}{2}} \times 2^{2x}}{2^x \times 2^{2x}} = 1$$

Numerator: $2^{\frac{3x}{2}} \times 2^{2x} = 2^{\frac{3x}{2} + \frac{4x}{2}} = 2^{\frac{7x}{2}}$
Denominator: $2^x \times 2^{2x} = 2^{x + 2x} = 2^{3x}$
The equation becomes:

$$\frac{2^{\frac{7x}{2}}}{2^{3x}} = 1$$

$$2^{\frac{7x}{2} - 3x} = 1$$

Simplify the exponent:

$$\frac{7x}{2} - 3x = \frac{7x}{2} - \frac{6x}{2} = \frac{x}{2}$$

So the equation is:

$$2^{\frac{x}{2}} = 1$$

Since $2^0 = 1$, we can equate the exponents:

$$\frac{x}{2} = 0$$ $$x = 0 \times 2$$ $$x = \boxed{0}$$