MCQ
The value of $\left(\frac{729}{4096}\right)^{\frac{-1}{3}}$ is
- ✓$\frac{16}{9}$
- B$\frac{-16}{9}$
- C$\frac{9}{16}$
- D$\frac{-9}{16}$
✓
Answer
Correct option: A.
$\frac{16}{9}$
$\left(\frac{729}{4096}\right)^{\frac{-1}{3}}=\left(\frac{4096}{729}\right)^{\frac{1}{3}}=\left(\frac{16^3}{9^3}\right)^{\frac{1}{3}}$
$=\frac{16^{3 \times \frac{1}{3}}}{9^{3 \times \frac{1}{3}}}$
$=\frac{16}{9}$
$=\frac{16^{3 \times \frac{1}{3}}}{9^{3 \times \frac{1}{3}}}$
$=\frac{16}{9}$
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