The expression $\sqrt[3]{125a^3}$ can be simplified by taking the cube root of each component separately.

1. The cube root of 125 is $\sqrt[3]{125} = 5$ because $5^3 = 125$.
2. The cube root of $a^3$ is $\sqrt[3]{a^3} = a$ because $(a)^3 = a^3$.

So, the simplified form of $\sqrt[3]{125a^3}$ is:

$\sqrt[3]{125a^3} = 5a$

Would you like more details on this process or have any questions?

Here are 5 related questions:

1. How do you simplify $\sqrt[3]{64b^6}$?
2. What is the cube root of $27x^3y^6$?
3. How do you solve $\sqrt[3]{8m^3n^9}$?
4. What is the general method for simplifying $\sqrt[3]{k^3}$?
5. How do you simplify expressions involving higher roots, such as $\sqrt[4]{81p^4}$?

Tip: Remember that the cube root of a product is the product of the cube roots, making it easier to simplify expressions like the one you provided.