Comparison of exponents

CAT 1997 Slot 1 · QA · Easy · Algebra

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Which of the following is true?

  1. A.

    7^{3^2} = (7^3)^2

  2. B.

    7^{3^2} > (7^3)^2

  3. C.

    7^{3^2} < (7^3)^2

  4. D.

    None of these

Answer

B

Explanation

Evaluate both expressions:

  1. 732=797^{3^2} = 7^9 since 32=93^2 = 9.
  2. (73)2=73×2=76(7^3)^2 = 7^{3 \times 2} = 7^6.

Since 79>767^9 > 7^6, we have 732>(73)27^{3^2} > (7^3)^2.

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