1) \( \frac{\left(2 a^{3} b^{4}\right)^{-5}}{\left(64 a^{-3} b^{2}\right)^{-1}} \)

To simplify the given expression, we'll start by rewriting it step by step: First, let's simplify the numerator: \((2 a^{3} b^{4})^{-5} = \frac{1}{(2 a^{3} b^{4})^{5}} = \frac{1}{2^{5} a^{15} b^{20}} = \frac{1}{32 a^{15} b^{20}}\). Now, simplify the denominator: \((64 a^{-3} b^{2})^{-1} = \frac{1}{64 a^{-3} b^{2}} = \frac{1}{64} a^{3} b^{-2}\). Now, we can rewrite the original expression as: \[ \frac{\frac{1}{32 a^{15} b^{20}}}{\frac{1}{64} a^{3} b^{-2}} = \frac{1}{32 a^{15} b^{20}} \times \frac{64}{a^{3} b^{-2}}. \] Next, simplify this: \[ = \frac{64}{32} \times \frac{1}{a^{15}} \times a^{3} \times \frac{1}{b^{20}} \times b^{2} = 2 \times a^{3 - 15} \times b^{2 - 20}. \] This simplifies to: \[ 2 a^{-12} b^{-18}. \] Finally, if we prefer to express negative exponents as positive, we can write: \[ \frac{2}{a^{12} b^{18}}. \] So the final answer is: \[ \frac{2}{a^{12} b^{18}}. \]