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Which expression is equivalent to 86×968^6 \times 9^6?\newlineChoices:\newline(A) 1726\frac{1}{72^6}\newline(B) 721272^{12}\newline(C) 72672^6\newline(D) 723672^{36}

Full solution

Q. Which expression is equivalent to 86×968^6 \times 9^6?\newlineChoices:\newline(A) 1726\frac{1}{72^6}\newline(B) 721272^{12}\newline(C) 72672^6\newline(D) 723672^{36}
  1. Recognize Property of Exponents: Recognize the property of exponents for multiplication. When multiplying powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. (a^m)(b^m) = (ab)^m
  2. Apply Property to Given Numbers: Apply the property to \(8^6 \times 9^6. Combine the bases 88 and 99, and keep the exponent 66. 86×96=(8×9)68^6 \times 9^6 = (8\times9)^6
  3. Calculate Product of Bases: Calculate the product of the bases 88 and 99. \newline8×9=728 \times 9 = 72
  4. Write Expression with Combined Base: Write the expression with the combined base and exponent.\newline(8×9)6=726(8\times9)^6 = 72^6
  5. Match Result with Choices: Match the result with the given choices. 72672^6 corresponds to choice (C) 72672^6.

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