Math Problem Statement
Solution
The question is asking for the simplified form of the expression .
Steps to Simplify:
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Break down the cube root: [ \sqrt[3]{a^5 \cdot b^4} = \sqrt[3]{a^5} \cdot \sqrt[3]{b^4} ]
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Simplify each term under the cube root:
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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 , which matches Option E.
Do you need more detailed clarification or have any other questions?
Related Questions:
- How do you simplify cube roots of higher powers like ?
- How can we apply this method to expressions with different exponents, such as ?
- What is the general rule for simplifying expressions like ?
- How do cube roots behave when we deal with negative exponents?
- 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!
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Math Problem Analysis
Mathematical Concepts
Exponents
Cube Roots
Algebraic Simplification
Formulas
∛(a^m * b^n) = ∛(a^m) * ∛(b^n)
∛(a^m) = a^(m/3)
Theorems
Exponentiation Theorem
Cube Root Properties
Suitable Grade Level
Grades 9-12
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