Simplify the expression: ([9]512 x [3]343 x sqrt(121)) / ((64)^(1)/(3) x (81)^(3)/(4) x (14641)^(1)/(4))

The numerator is $\sqrt[9]{512} \times \sqrt[3]{343} \times \sqrt{121}$.
We find the roots:

$$\sqrt[9]{512} = \sqrt[9]{2^9} = 2$$ $$\sqrt[3]{343} = \sqrt[3]{7^3} = 7$$ $$\sqrt{121} = \sqrt{11^2} = 11$$

Multiply these values to get the numerator's value:

$$2 \times 7 \times 11 = 14 \times 11 = 154$$

The denominator is $(64)^{\frac{1}{3}} \times (81)^{\frac{3}{4}} \times (14641)^{\frac{1}{4}}$.
We simplify each term using exponent rules $(a^m)^n = a^{mn}$:

$$(64)^{\frac{1}{3}} = (4^3)^{\frac{1}{3}} = 4^{3 \times \frac{1}{3}} = 4^1 = 4$$ $$(81)^{\frac{3}{4}} = (3^4)^{\frac{3}{4}} = 3^{4 \times \frac{3}{4}} = 3^3 = 27$$ $$(14641)^{\frac{1}{4}} = (11^4)^{\frac{1}{4}} = 11^{4 \times \frac{1}{4}} = 11^1 = 11$$

Multiply these values to get the denominator's value:

$$4 \times 27 \times 11 = 108 \times 11 = 1188$$

$$\frac{154}{1188}$$

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor. Both are divisible by 11:

$$\frac{154 \div 11}{1188 \div 11} = \frac{14}{108}$$

Both are divisible by 2:

$$\frac{14 \div 2}{108 \div 2} = \frac{7}{54}$$

The final answer is $\frac{7}{54}$.