Simplify \(\frac{9^{\frac{1}{3}} \times 27^{-\frac{1}{3}}}{3^{-\frac{1}{6}} \times 3^{\frac{2}{3}}}\)
 

  • A \(\frac{1}{3}\)
  • B 1
  • C 3
  • D 9
jamb 1986mathematics

The correct answer is B. 1

\(\frac{9^{\frac{1}{3}} \times 27^{-\frac{1}{3}}}{3^{-\frac{1}{6}} \times 3^{\frac{2}{3}}}\)

= \(\frac{(3^2)^{\frac{1}{3}} \times (3^3)^{-\frac{1}{3}}}{3^{-\frac{1}{6}} \times 3^{\frac{2}{3}}}\)

= \(\frac{3^{\frac{2}{3}} \times 3^{\frac{2}{3}}}{3^{-\frac{1}{6}} \times 3^{\frac{2}{3}}}\)

= \(\frac{3^{\frac{5}{6}}}{3^{-\frac{5}{6}}}\)

= 1

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