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Which expression is equivalent to 6×636 \times 6^3?\newlineChoices:\newline(A) 164\frac{1}{6^4}\newline(B) 163\frac{1}{6^3}\newline(C) 646^4\newline(D) 636^3

Full solution

Q. Which expression is equivalent to 6×636 \times 6^3?\newlineChoices:\newline(A) 164\frac{1}{6^4}\newline(B) 163\frac{1}{6^3}\newline(C) 646^4\newline(D) 636^3
  1. Understand the problem: Understand the problem.\newlineWe need to find an expression equivalent to the multiplication of 66 by 66 raised to the power of 33.
  2. Apply exponent rule: Apply the exponent rule for multiplication aman=a(m+n)a^m * a^n = a^{(m+n)}. 663=6163=6(1+3)=646 * 6^3 = 6^1 * 6^3 = 6^{(1+3)} = 6^4
  3. Match with choices: Match the result with the given choices.\newlineThe expression 646^4 matches with choice (C) 646^4.

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