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Evaluate. 23−1283=\dfrac{\sqrt[3]{2}}{\sqrt[3]{-128}}=

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Domain and range of exponential and logarithmic functionsright chevron icon

Full solution

Q. Evaluate. 23−1283=\dfrac{\sqrt[3]{2}}{\sqrt[3]{-128}}=
  1. Simplify cube roots: Simplify the cube roots.\newline23=21/3 \sqrt[3]{2} = 2^{1/3} \newline−1283=−1281/3 \sqrt[3]{-128} = -128^{1/3}
  2. Simplify −128-128: \newlineStep 22: Simplify −1283\sqrt[3]{-128}.\newline−128=−27 -128 = -2^7 \newline−1283=−273=−27/3 \sqrt[3]{-128} = \sqrt[3]{-2^7} = -2^{7/3}
  3. Divide cube roots: \newlineStep 33: Divide the cube roots.\newline21/3−27/3=21/3−7/3=2−6/3=2−2 \dfrac{2^{1/3}}{-2^{7/3}} = 2^{1/3 - 7/3} = 2^{-6/3} = 2^{-2}
  4. Simplify exponent: \newlineStep 44: Simplify the exponent.\newline2−2=122=14 2^{-2} = \dfrac{1}{2^2} = \dfrac{1}{4}

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