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The question is asking for the simplified form of the expression \( \sqrt[3]{a^5 \cdot b^4} \).

### Steps to Simplify:
1. **Break down the cube root**: 
   \[
   \sqrt[3]{a^5 \cdot b^4} = \sqrt[3]{a^5} \cdot \sqrt[3]{b^4}
   \]

2. **Simplify each term under the cube root**:
   - \( \sqrt[3]{a^5} = a^{5/3} = a^1 \cdot a^{2/3} \)
   - \( \sqrt[3]{b^4} = b^{4/3} = b^1 \cdot b^{1/3} \)

3. **Combine the simplified terms**:
   \[
   a^{1} \cdot b^{1} \cdot \sqrt[3]{a^2 \cdot b} = ab \cdot \sqrt[3]{a^2 \cdot b}
   \]

### Final Simplified Form:
The correct simplified form is \( ab \cdot \sqrt[3]{a^2 \cdot b} \), which matches **Option E**.

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Do you need more detailed clarification or have any other questions?

### Related Questions:
1. How do you simplify cube roots of higher powers like \( \sqrt[3]{a^7} \)?
2. How can we apply this method to expressions with different exponents, such as \( \sqrt[4]{a^8 \cdot b^2} \)?
3. What is the general rule for simplifying expressions like \( \sqrt[n]{a^m \cdot b^p} \)?
4. How do cube roots behave when we deal with negative exponents?
5. How can we solve cube root problems without breaking them down into individual terms?

**Tip:** Always break down roots into simpler powers and apply the exponent rules carefully!

Bentuk sederhana dari ∛(a⁵.b⁴) adalah ...

Learn how to simplify the expression ∛(a⁵.b⁴) using exponent and cube root rules. This problem involves breaking down each term under the cube root, applying exponentiation properties, and simplifying the result. Ideal for students in Grades 9-12.

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