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Which expression is equivalent to 35×253^5 \times 2^5?\newlineChoices:\newline(A) 6106^{10}\newline(B) 656^5\newline(C) 6256^{25}\newline(D) 165\frac{1}{6^5}

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Full solution

Q. Which expression is equivalent to 35×253^5 \times 2^5?\newlineChoices:\newline(A) 6106^{10}\newline(B) 656^5\newline(C) 6256^{25}\newline(D) 165\frac{1}{6^5}
  1. Recognize operation: Step 11: Recognize the operation between 353^5 and 252^5. We are multiplying two powers with different bases but the same exponents.
  2. Apply rule for multiplication: Step 22: Apply the rule for multiplying powers with the same exponent.\newline(35)×(25)=(3×2)5=65(3^5) \times (2^5) = (3\times2)^5 = 6^5.
  3. Match with choices: Step 33: Match the result with the given choices. 656^5 corresponds to choice (B).

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