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Mathematics

The value of [{(−13)−2}−1]2\Big[\Big\lbrace\Big(\dfrac{-1}{3}\Big)^{-2}\Big\rbrace^{-1}\Big]^{2} is

  1. 81

  2. -81

  3. 181\dfrac{1}{81}

  4. −181-\dfrac{1}{81}

Exponents

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Answer

Given:

[{(−13)−2}−1]2\Big[\Big\lbrace\Big(\dfrac{-1}{3}\Big)^{-2}\Big\rbrace^{-1}\Big]^{2}

Multiply the exponents: (-2) x (-1) x 2 = 4. \quad [Power of power rule]

∴ (−13)4=(−1)434=181\Big(\dfrac{-1}{3}\Big)^4 = \dfrac{(-1)^4}{3^4} = \dfrac{1}{81}

Hence, option 3 is the correct option.

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