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Which expression is equivalent to (36)9(3^6)^9?\newlineChoices:\newline(A) 3153^{15}\newline(B) 1315\frac{1}{3^{15}}\newline(C) 1354\frac{1}{3^{54}}\newline(D) 3543^{54}

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Identify equivalent exponential expressions Iright chevron icon

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Q. Which expression is equivalent to (36)9(3^6)^9?\newlineChoices:\newline(A) 3153^{15}\newline(B) 1315\frac{1}{3^{15}}\newline(C) 1354\frac{1}{3^{54}}\newline(D) 3543^{54}
  1. Apply power rule: Apply the power of a power rule.\newlineWhat operation should we perform with the exponents, 66 and 99?\newlineWhen we raise a power to another power, we multiply the exponents.\newline(am)n=a(m×n)(a^m)^n = a^{(m \times n)}
  2. Calculate new exponent: Calculate the new exponent by multiplying the exponents 66 and 99. \newline(36)9=3(6×9)(3^6)^9 = 3^{(6 \times 9)}\newline=354= 3^{54}
  3. Choose equivalent expression: Choose the equivalent expression for (36)9(3^6)^9.(36)9=354(3^6)^9 = 3^{54} The equivalent expression is 3543^{54}.

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