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Simplify. Express your answer using a single exponent.\newline(6a3)2(6a^3)^2

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Q. Simplify. Express your answer using a single exponent.\newline(6a3)2(6a^3)^2
  1. Apply power rule: Apply the power of a power rule.\newlineThe power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have (6a3)2(6a^3)^2, which means we need to square both the coefficient 66 and the variable term a3a^3.\newline(6a3)2=62×(a3)2(6a^3)^2 = 6^2 \times (a^3)^2
  2. Calculate coefficient square: Calculate the square of the coefficient 66.\ To find 626^2, we multiply 66 by itself.\ 62=6×6=366^2 = 6 \times 6 = 36
  3. Calculate variable term square: Calculate the square of the variable term a3a^3. To find (a3)2(a^3)^2, we multiply the exponent 33 by the exponent 22. (a3)2=a(3×2)=a6(a^3)^2 = a^{(3 \times 2)} = a^6
  4. Combine results: Combine the results from Step 22 and Step 33.\newlineNow we combine the squared coefficient and the squared variable term to get the final simplified expression.\newline(6a3)2=36×a6(6a^3)^2 = 36 \times a^6

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