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.

Learn how to simplify the cube root of 125a³ with a detailed step-by-step solution. This problem covers key algebraic concepts, including cube roots and the simplification of radicals, suitable for students in Grades 7-8.

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