Simplify the expression $(\frac{u^3}{v^6})^5$.

1. Problem Description

Simplify the expression $(\frac{u^3}{v^6})^5$.

2. Solution Steps

We use the power of a quotient rule: $(\frac{a}{b})^n = \frac{a^n}{b^n}$.

$(\frac{u^3}{v^6})^5 = \frac{(u^3)^5}{(v^6)^5}$

Then, we use the power of a power rule: $(a^m)^n = a^{m \cdot n}$.

$\frac{(u^3)^5}{(v^6)^5} = \frac{u^{3 \cdot 5}}{v^{6 \cdot 5}} = \frac{u^{15}}{v^{30}}$.

3. Final Answer

$\frac{u^{15}}{v^{30}}$