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Which expression is equivalent to 54×585^4 \times 5^8?\newlineChoices:\newline(A) 1532\frac{1}{5^{32}}\newline(B) 5325^{32}\newline(C) 5125^{12}\newline(D) 1512\frac{1}{5^{12}}

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Q. Which expression is equivalent to 54×585^4 \times 5^8?\newlineChoices:\newline(A) 1532\frac{1}{5^{32}}\newline(B) 5325^{32}\newline(C) 5125^{12}\newline(D) 1512\frac{1}{5^{12}}
  1. Identify Operation: Identify the operation to perform with the exponents.\newlineWhen we multiply powers with the same base, we add the exponents.\newlineam×an=a(m+n)a^m \times a^n = a^{(m+n)}
  2. Add Exponents: Add the exponents of the powers of 55. \newline54×58=54+85^4 \times 5^8 = 5^{4+8}\newlineCalculate the sum of the exponents.\newline54+8=5125^{4+8} = 5^{12}
  3. Calculate Sum: Match the result with the given choices.\newlineThe expression 5125^{12} corresponds to choice (C) 5125^{12}.

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