Simplify the expression [(21)/(3) x 8^(2)/(3) x 6^(5)/(4) x 3^(3)/(4)9-1 x [3]16]⁻⁴ to find the value of x.

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).
$8 = 2^3$
$6 = 2 \times 3$
$9 = 3^2$
$\sqrt[3]{16} = 16^{\frac{1}{3}} = (2^4)^{\frac{1}{3}} = 2^{\frac{4}{3}}$

Step 2: Substitute these prime factor expressions into the equation.

$$x = \left[\frac{2^{\frac{1}{3}} \times (2^3)^{\frac{2}{3}} \times (2 \times 3)^{\frac{5}{4}} \times 3^{\frac{3}{4}}}{(3^2)^{-1} \times 2^{\frac{4}{3}}}\right]^{-4}$$

Step 3: Apply exponent rules $(a^m)^n = a^{mn}$ and $(ab)^n = a^n b^n$ to simplify terms.

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