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Mathematics

The value of (2-1 × 22 × 2-3 × 24 × 2-5 × 26 × 2-7 × 28 × 2-9 × 210)-1 is:

  1. 2

  2. 16

  3. 132\dfrac{1}{32}

  4. 32

Indices

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Answer

Given,

⇒ (2-1 × 22 × 2-3 × 24 × 2-5 × 26 × 2-7 × 28 × 2-9 × 210)-1

⇒ [2(-1 + 2 - 3 + 4 - 5 + 6 - 7 + 8 - 9 + 10)]-1

⇒ [2(-1 - 3 - 5 - 7 - 9 + 2 + 4 + 6 + 8 + 10)]-1

⇒ [2(-25 + 30)]-1

⇒ (25)-1

⇒ 2-5

⇒ 125\dfrac{1}{2^5}

⇒ 132\dfrac{1}{32}.

Hence, option 3 is the correct option.

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