If \(\rm x^{-\frac{4}{5}}=81\) then x = ?

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Patna High Court Mazdoor Official Paper (Held On: 22 Jun, 2025)
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  1. \(\frac{1}{243}\)
  2. 243
  3. \(\frac{1}{3}\)
  4. 3

Answer (Detailed Solution Below)

Option 2 : 243
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Detailed Solution

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Given:

x-4/5 = 81

Formula used:

To solve for x: x-n = a ⟹ x = a-1/n

Calculation:

x-4/5 = 81

⇒ x = 81-1/(-4/5)

⇒ x = 815/4

⇒ x = (34)5/4

⇒ x = 3(4×5/4)

⇒ x = 35

⇒ x = 243

∴ The correct answer is option (2).

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