Simplify the expression: (64^(2/3) cbrt(125) (2 (1/5))^(-3)) / (42 fourthrt(625))

The numerator is $64^{\frac{2}{3}} \times \sqrt[3]{125} \times \left(2 \times \frac{1}{5}\right)^{-3}$.
Simplify each part:

$$64^{\frac{2}{3}} = (4^3)^{\frac{2}{3}} = 4^{3 \times \frac{2}{3}} = 4^2 = 16$$ $$\sqrt[3]{125} = \sqrt[3]{5^3} = 5$$ $$\left(2 \times \frac{1}{5}\right)^{-3} = \left(\frac{2}{5}\right)^{-3} = \left(\frac{5}{2}\right)^3 = \frac{5^3}{2^3} = \frac{125}{8}$$

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

$$16 \times 5 \times \frac{125}{8} = 80 \times \frac{125}{8} = \frac{80}{8} \times 125 = 10 \times 125 = 1250$$

The denominator is $4^2 \times \sqrt[4]{625}$.
Simplify each part:

$$4^2 = 16$$ $$\sqrt[4]{625} = \sqrt[4]{5^4} = 5$$

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

$$16 \times 5 = 80$$

$$\frac{1250}{80}$$

Simplify the fraction by dividing both numerator and denominator by 10:

$$\frac{125}{8}$$

This fraction cannot be simplified further.