Simplify the expression $\left(\frac{p^3}{5q}\right)^3$.

1. Problem Description

Simplify the expression $\left(\frac{p^3}{5q}\right)^3$.

2. Solution Steps

We need to simplify the given expression. We use the property of exponents that states $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ and $(a^m)^n = a^{mn}$.

$\left(\frac{p^3}{5q}\right)^3 = \frac{(p^3)^3}{(5q)^3}$

Now, we simplify the numerator:

$(p^3)^3 = p^{3 \times 3} = p^9$

Next, we simplify the denominator:

$(5q)^3 = 5^3 \cdot q^3 = 125q^3$

Therefore, the simplified expression is:

$\frac{p^9}{125q^3}$

3. Final Answer

$\frac{p^9}{125q^3}$