Question

1. $(2v^{-9})^{10}$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$, so $(2v^{-9})^{10}=2^{10} \cdot (v^{-9})^{10}$

Step2: Calculate $2^{10}$

$2^{10}=1024$

Step3: Apply power of a power rule

$(a^m)^n=a^{m \cdot n}$, so $(v^{-9})^{10}=v^{-9 \times 10}=v^{-90}$

Step4: Rewrite positive exponent (optional)

$v^{-90}=\frac{1}{v^{90}}$

Answer:

$1024v^{-90}$ or $\frac{1024}{v^{90}}$