Simplify (24 imes 36)^ rac12 imes [3]8 x sqrt(81) / (16^ rac34 imes 27^ rac13).

The numerator is $(2^4 \times 36)^{\frac{1}{2}} \times \sqrt[3]{8} \times \sqrt{81}$.
Simplify each part:

$$(2^4 \times 36)^{\frac{1}{2}} = (2^4)^{\frac{1}{2}} \times (36)^{\frac{1}{2}} = 2^{4 \times \frac{1}{2}} \times \sqrt{36} = 2^2 \times 6 = 4 \times 6 = 24$$ $$\sqrt[3]{8} = \sqrt[3]{2^3} = 2$$ $$\sqrt{81} = \sqrt{9^2} = 9$$

Multiply these simplified terms to get the numerator's value:

$$24 \times 2 \times 9 = 48 \times 9 = 432$$

The denominator is $16^{\frac{3}{4}} \times 27^{\frac{1}{3}}$.
Simplify each part:

$$16^{\frac{3}{4}} = (2^4)^{\frac{3}{4}} = 2^{4 \times \frac{3}{4}} = 2^3 = 8$$ $$27^{\frac{1}{3}} = (3^3)^{\frac{1}{3}} = 3^{3 \times \frac{1}{3}} = 3^1 = 3$$

Multiply these simplified terms to get the denominator's value:

$$8 \times 3 = 24$$

$$\frac{432}{24}$$

Perform the division:

$$432 \div 24 = 18$$

The final answer is 18.