Question

1. (2v⁴)⁻³

Explanation:

Step1: Apply power of a product rule

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

Step2: Simplify negative exponent for constant

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

Step4: Rewrite negative variable exponent

$v^{-12} = \frac{1}{v^{12}}$, then combine terms
$\frac{1}{8} \cdot \frac{1}{v^{12}} = \frac{1}{8v^{12}}$

Answer:

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