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Simplify. Express your answer using a single exponent.\newline(3x6)2(3x^6)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(3x6)2(3x^6)^2
  1. Apply Power to Factors: Apply the power to each factor within the parentheses.\newlineWhen raising a power to a product, we distribute the exponent to each factor within the product.\newline(3x6)2=32×(x6)2(3x^6)^2 = 3^2 \times (x^6)^2
  2. Simplify 323^2: Simplify 323^2. \newline32=3×3=93^2 = 3 \times 3 = 9
  3. Simplify (x6)2(x^6)^2: Simplify (x6)2(x^6)^2. When raising a power to another power, we multiply the exponents. (x6)2=x(6×2)=x12(x^6)^2 = x^{(6 \times 2)} = x^{12}
  4. Combine Simplified Terms: Combine the simplified terms to write the final answer.\newline(3x6)2=32×(x6)2=9×x12=9x12(3x^6)^2 = 3^2 \times (x^6)^2 = 9 \times x^{12} = 9x^{12}

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