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root(3)(-6x^(5))*root(3)(18x^(4))

2424. −6x53⋅18x43 \sqrt[3]{-6 x^{5}} \cdot \sqrt[3]{18 x^{4}}

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Full solution

Q. 2424. −6x53⋅18x43 \sqrt[3]{-6 x^{5}} \cdot \sqrt[3]{18 x^{4}}
  1. Identify Properties: Identify the properties of cube roots to simplify the expression. −6x53⋅18x43\sqrt[3]{-6x^{5}} \cdot \sqrt[3]{18x^{4}} can be combined using the product rule for radicals.
  2. Combine Cube Roots: Combine the cube roots. −6x5⋅18x43\sqrt[3]{-6x^{5} \cdot 18x^{4}}
  3. Multiply and Factor: Multiply the coefficients and the like terms inside the cube root. −108x93\sqrt[3]{-108x^{9}}
  4. Separate Perfect Cubes: Factor inside the cube root to find perfect cubes. −27⋅4⋅x93\sqrt[3]{-27 \cdot 4 \cdot x^{9}}
  5. Calculate Cube Roots: Separate the perfect cube factors.\newline−273×43×x93\sqrt[3]{-27} \times \sqrt[3]{4} \times \sqrt[3]{x^{9}}
  6. Combine Results: Calculate the cube root of each factor. −273=−3\sqrt[3]{-27} = -3, 43\sqrt[3]{4} is not a perfect cube, and x93=x3\sqrt[3]{x^{9}} = x^{3}.
  7. Simplify Further: Combine the results.\newline−3×43×x3-3 \times \sqrt[3]{4} \times x^{3}
  8. Final Answer: Realize that 43\sqrt[3]{4} cannot be simplified further.\newlineThe final answer is −3×43×x3-3 \times \sqrt[3]{4} \times x^{3}.

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