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Which expression is equivalent to 35×393^5 \times 3^9?\newlineChoices:\newline(A) 3453^{45}\newline(B) 1345\frac{1}{3^{45}}\newline(C) 3143^{14}\newline(D) 1314\frac{1}{3^{14}}

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Q. Which expression is equivalent to 35×393^5 \times 3^9?\newlineChoices:\newline(A) 3453^{45}\newline(B) 1345\frac{1}{3^{45}}\newline(C) 3143^{14}\newline(D) 1314\frac{1}{3^{14}}
  1. Identify Base and Exponents: Identify the base and the exponents.\newlineIn 353^5 and 393^9, 33 is the base raised to the exponents 55 and 99 respectively.\newlineBase: 33\newlineExponents: 55, 99
  2. Rewrite Expression as Single Power: Given expression: 35×393^5 \times 3^9\newlineRewrite this expression as a single power of 33.\newlineWhen we multiply powers with the same base, we add the exponents.\newline35×393^5 \times 3^9\newline=35+9= 3^{5+9}\newline=314= 3^{14}
  3. Choose Equivalent Expression: Choose the equivalent expression for 35×393^5 \times 3^9. From the previous step, we have determined that 35×393^5 \times 3^9 is equal to 3143^{14}. Therefore, the equivalent expression is 3143^{14}.

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