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root(3)(((8)/(21))^(4))

(821)43 \sqrt[3]{\left(\frac{8}{21}\right)^{4}}

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Full solution

Q. (821)43 \sqrt[3]{\left(\frac{8}{21}\right)^{4}}
  1. Calculate Powers: Calculate the fourth power of the numerator and denominator separately.\newline(84)/(214)(8^4) / (21^4)
  2. Compute Fourth Power: Compute the fourth power of 88 and 2121.\newline84=40968^4 = 4096\newline214=19448121^4 = 194481
  3. Place Under Cube Root: Place the calculated powers under the cube root. 40961944813\sqrt[3]{\frac{4096}{194481}}
  4. Simplify Cube Root: Simplify the cube root of the numerator and denominator.40963=16\sqrt[3]{4096} = 161944813=58\sqrt[3]{194481} = 58

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