MCQ
Value of $\sqrt[4]{(81)^{-2}}$ is
- ✓$\frac{1}{9}$
- B$\frac{1}{3}$
- C9
- D$\frac{1}{81}$
✓
Answer
Correct option: A.
$\frac{1}{9}$
(a)
$\sqrt[4]{(81)^{-2}}=\sqrt[4]{\left(3^4\right)^{-2}}=\sqrt[4]{3^{4 \times-2}}=\left(3^{-8}\right)^{1 / 4}=3^{-8 \times \frac{1}{4}}=3^{-2}=\frac{1}{3^2}=\frac{1}{9}$
$\sqrt[4]{(81)^{-2}}=\sqrt[4]{\left(3^4\right)^{-2}}=\sqrt[4]{3^{4 \times-2}}=\left(3^{-8}\right)^{1 / 4}=3^{-8 \times \frac{1}{4}}=3^{-2}=\frac{1}{3^2}=\frac{1}{9}$
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