If (1/5)^{3y} = 0.008, then find the value of (0.25) y .

2017

If (1/5)^{3y} = 0.008, then find the value of (0.25) y .

Answer: D. 0.25 — Key observation: 0.008 = 8/1000 = 1/125 = (1/5)^3. Step 1: Equate the exponents using the same base. Since (1/5)^{3y} = (1/5)^3, we have 3y = 3. So y = 1. Now…

  1. A.

    1.00

  2. B.

    0.75

  3. C.

    0.50

  4. D.

    0.25

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Correct answer: D

Key observation: 0.008 = 8/1000 = 1/125 = (1/5)^3.

Step 1: Equate the exponents using the same base.

  • Since (1/5)^{3y} = (1/5)^3, we have 3y = 3.

  • So y = 1.

  • Now compute (0.25)^y = (0.25)^1 = 0.25.

Final answer: 0.25

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