Simplify the expression [ (2^(1/3) 8^(2/3) 6^(5/4) 3^(3/4)) / (9⁻¹ 16^(1/3)) ] ^ -4

To find the value of $x$, we need to simplify the expression using the rules of exponents.

The given expression is:

$$x = \left[\frac{2^{\frac{1}{3}} \times 8^{\frac{2}{3}} \times 6^{\frac{5}{4}} \times 3^{\frac{3}{4}}}{9^{-1} \times \sqrt[3]{16}}\right]^{-4}$$

Step 1: Express all numbers as powers of their prime factors (2 and 3).
$8 = 2^3$
$6 = 2 \times 3$
$9 = 3^2$
$\sqrt[3]{16} = 16^{\frac{1}{3}}