Solve this multiple-choice question and choose the correct option.

Concept / Approach For the same base, add exponents when multiplying: a^m × a^n = a^(m + n). Convert the result using prime factorization of the base. Step-by-step calculation(256)^0.16 × (256)^0.09 = 256^(0.16 + 0.09) = 256^0.25256 = 2^8 ⇒ 256^0.25 = (2^8)^(1/4) = 2^(8/4) = 2^2 = 4 Final Answer4

Curioustab

Compute: (256)^0.16 × (256)^0.09

Aptitude Surds and Indices Difficulty: Easy

Choose an option

A

2
B

4
C

8
D

16

Answer

Correct Answer: 4

Explanation

Concept / Approach

For the same base, add exponents when multiplying: a^m × a^n = a^(m + n).
Convert the result using prime factorization of the base.

Step-by-step calculation(256)^0.16 × (256)^0.09 = 256^(0.16 + 0.09) = 256^0.25256 = 2^8 ⇒ 256^0.25 = (2^8)^(1/4) = 2^(8/4) = 2^2 = 4

Final Answer4

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