The expression $\sqrt[3]{125a^3}$ simplifies as follows:

[ \sqrt[3]{125a^3} = \sqrt[3]{125} \times \sqrt[3]{a^3} ]

• The cube root of 125 is 5 because $5^3 = 125$.
• The cube root of $a^3$ is $a$.

Therefore:

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

Would you like more details or have any questions?

Here are 5 related questions to explore:

1. What is $\sqrt[3]{64a^6}$?
2. How do you simplify $\sqrt[3]{216b^3}$?
3. What is the cube root of $343c^9$?
4. How do you simplify $\sqrt[3]{1000d^3}$?
5. What happens if the exponent inside the cube root is not a multiple of 3?

Tip: When simplifying cube roots, focus on finding perfect cubes inside the radicand to make the process easier.