Question
Write the correct answer in the following:
Value of $\sqrt[4]{(81)^{-2}}$ is.
Value of $\sqrt[4]{(81)^{-2}}$ is.
✓
Answer
- $\frac{1}{9}$
Solution:
$\sqrt[4]{(81)^{-2}}=\sqrt[4]{\Big(\frac{1}{81}\Big)^2}=\sqrt[4]{\Big\{\Big(\frac{1}{9}\Big)^2\Big\}^2}=\sqrt[4]{\Big(\frac{1}{9}\Big)^4}=\Big(\frac{1}{9}\Big)^{4\times\frac{1}{4}}=\frac{1}{9}$
Hence, (a) is the correct answer.
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