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Simplify each cube root by factoring out perfect cubes.

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Answer

3523\frac{3}{5}\sqrt[3]{2}

Step-by-step solution

5 steps

  1. Simplify each cube root by factoring out perfect cubes.

    163=8×23=23×23=223\sqrt[3]{16} = \sqrt[3]{8 \times 2} = \sqrt[3]{2^3 \times 2} = 2\sqrt[3]{2} 1283=64×23=43×23=423\sqrt[3]{128} = \sqrt[3]{64 \times 2} = \sqrt[3]{4^3 \times 2} = 4\sqrt[3]{2} 543=27×23=33×23=323\sqrt[3]{54} = \sqrt[3]{27 \times 2} = \sqrt[3]{3^3 \times 2} = 3\sqrt[3]{2}

  2. Substitute the simplified cube roots back into the original expression.

    12(223)−35(423)−7(323)12(2\sqrt[3]{2}) - \frac{3}{5}(4\sqrt[3]{2}) - 7(3\sqrt[3]{2})

  3. Multiply the coefficients for each term.

    2423−12523−212324\sqrt[3]{2} - \frac{12}{5}\sqrt[3]{2} - 21\sqrt[3]{2}

  4. Combine the terms with 23\sqrt[3]{2} by adding or subtracting their coefficients.

    (24−125−21)23\left(24 - \frac{12}{5} - 21\right)\sqrt[3]{2}

  5. Perform the arithmetic on the coefficients.

    (3−125)23\left(3 - \frac{12}{5}\right)\sqrt[3]{2}

    To subtract the fraction, find a common denominator:

    (3×55−125)23=(155−125)23\left(\frac{3 \times 5}{5} - \frac{12}{5}\right)\sqrt[3]{2} = \left(\frac{15}{5} - \frac{12}{5}\right)\sqrt[3]{2} (15−125)23=3523\left(\frac{15 - 12}{5}\right)\sqrt[3]{2} = \frac{3}{5}\sqrt[3]{2}

    The final answer is 3523\frac{3}{5}\sqrt[3]{2}.

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