MCQ
$\frac{9^{1 / 3} \times 27^{-1 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}$ is equal to
- ✓$3^{-1 / 3}$
- B$3^{1 / 3}$
- C3
- D$3^{2 / 3}$
✓
Answer
Correct option: A.
$3^{-1 / 3}$
(a)
$\frac{9^{1 / 3} \times 27^{-1 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}=\frac{\left(3^2\right)^{1 / 3} \times\left(3^3\right)^{-1 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}=\frac{3^{2 / 3} \times 3^{-3 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}=\frac{3^{\frac{2}{3}-\frac{3}{2}}}{3^{\frac{1}{6}-\frac{2}{3}}}=\frac{3^{-5 / 6}}{3^{-1 / 2}}=3^{-\frac{5}{6}-\frac{1}{2}}=3^{-\frac{1}{3}}$
$\frac{9^{1 / 3} \times 27^{-1 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}=\frac{\left(3^2\right)^{1 / 3} \times\left(3^3\right)^{-1 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}=\frac{3^{2 / 3} \times 3^{-3 / 2}}{3^{1 / 6} \times 3^{-2 / 3}}=\frac{3^{\frac{2}{3}-\frac{3}{2}}}{3^{\frac{1}{6}-\frac{2}{3}}}=\frac{3^{-5 / 6}}{3^{-1 / 2}}=3^{-\frac{5}{6}-\frac{1}{2}}=3^{-\frac{1}{3}}$
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