Question

\\2u^3 \cdot (2v^{-4})^3\\

Explanation:

Expand the power of the monomial

$$ (2v^{-4})^3 = 2^3 \cdot (v^{-4})^3 = 8v^{-12} $$

Multiply the expressions

$$ 2u^3 \cdot 8v^{-12} = 16u^3v^{-12} $$

Simplify using positive exponents

$$ 16u^3v^{-12} = \frac{16u^3}{v^{12}} $$

Answer:

$$\frac{16u^3}{v^{12}}$$