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.

Understand how to simplify the cube root expression ³√125a³ step by step. This problem explores key algebraic concepts like cube roots and radicals, suitable for students in Grades 7-9.

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