Question

1. $(2x^4)^{-3}$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so $(2x^4)^{-3} = 2^{-3} \cdot (x^4)^{-3}$

Step2: Apply negative exponent rule

$a^{-n} = \frac{1}{a^n}$, so $2^{-3} = \frac{1}{2^3} = \frac{1}{8}$

Step3: Apply power of a power rule

$(a^m)^n = a^{m \cdot n}$, so $(x^4)^{-3} = x^{4 \cdot (-3)} = x^{-12} = \frac{1}{x^{12}}$

Step4: Multiply the results

Multiply the two simplified terms: $\frac{1}{8} \cdot \frac{1}{x^{12}}$

Answer:

$\frac{1}{8x^{12}}$