Question

1. $(2x^{-4})^{-4} cdot 2x^{-1}$

Explanation:

Step1: Apply power of a product rule

$(2x^{-4})^{-4} = 2^{-4} \cdot (x^{-4})^{-4}$

Step2: Simplify exponents

$2^{-4} = \frac{1}{2^4} = \frac{1}{16}$; $(x^{-4})^{-4} = x^{(-4)\times(-4)} = x^{16}$

Step3: Rewrite the original expression

$\frac{1}{16}x^{16} \cdot 2x^{-1}$

Step4: Multiply coefficients and combine x terms

$\frac{1}{16} \times 2 = \frac{2}{16} = \frac{1}{8}$; $x^{16} \cdot x^{-1} = x^{16+(-1)} = x^{15}$

Answer:

$\frac{1}{8}x^{15}$