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Which expression is equivalent to 59×575^9 \times 5^7?\newlineChoices:\newline(A) 5635^{63}\newline(B) 1563\frac{1}{5^{63}}\newline(C) 5165^{16}\newline(D) 1516\frac{1}{5^{16}}

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Full solution

Q. Which expression is equivalent to 59×575^9 \times 5^7?\newlineChoices:\newline(A) 5635^{63}\newline(B) 1563\frac{1}{5^{63}}\newline(C) 5165^{16}\newline(D) 1516\frac{1}{5^{16}}
  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 55.59×575^9 \times 5^7=5(9+7)= 5^{(9+7)}=516= 5^{16}
  3. Match Result: Match the result with the given choices.\newlineThe expression 5165^{16} corresponds to choice (C).

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