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Indices and Exponential Equations Statements

CMAT 2023 · Quantitative Techniques & Data Interpretation · Medium · Algebra

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Given below are two statements:

Statement I: (243)0.16×(9)0.1=0.3(243)^{0.16} \times (9)^{0.1} = 0.3

Statement II: If 3.105×10P=0.00239+0.0007153.105 \times 10^P = 0.00239 + 0.000715, then P=−3P = -3

In the light of the above statements choose the most appropriate answer from the options given below:

  1. A.

    Both Statement I and Statement II are correct

  2. B.

    Both Statement I and Statement II are incorrect

  3. C.

    Statement I is correct but Statement II is incorrect

  4. D.

    Statement I is incorrect but Statement II is correct

Answer

D

Explanation

Statement I: (243)0.16×(9)0.1=(35)0.16×(32)0.1=30.8×30.2=31=3≠0.3(243)^{0.16} \times (9)^{0.1} = (3^5)^{0.16} \times (3^2)^{0.1} = 3^{0.8} \times 3^{0.2} = 3^1 = 3 \neq 0.3 So Statement I is incorrect.

Statement II: 0.00239+0.000715=0.003105=3.105×10−30.00239 + 0.000715 = 0.003105 = 3.105 \times 10^{-3} Therefore, P=−3P = -3. Statement II is correct.

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