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Which expression is equivalent to (46)2(4^6)^2?\newlineChoices:\newline(A) 148\frac{1}{4^8}\newline(B) 4124^{12}\newline(C) 484^8\newline(D) 1412\frac{1}{4^{12}}

Full solution

Q. Which expression is equivalent to (46)2(4^6)^2?\newlineChoices:\newline(A) 148\frac{1}{4^8}\newline(B) 4124^{12}\newline(C) 484^8\newline(D) 1412\frac{1}{4^{12}}
  1. Apply Power of a Power Rule: Simplify the expression using the power of a power rule, which states (am)n=amn(a^m)^n = a^{m*n}.\newlineCalculation: (46)2=462=412(4^6)^2 = 4^{6*2} = 4^{12}.
  2. Compare with Choices: Compare the result with the given choices.\newlineCalculation: 4124^{12} matches choice (B) 412.4^{12}.

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