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Simplify. Express your answer using a single exponent.\newline(4d6)3(4d^6)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4d6)3(4d^6)^3
  1. Apply power rule: Apply the power of a power rule to the expression (4d6)3(4d^6)^3. The power of a power rule states that when raising a power to another power, you multiply the exponents. For the coefficient 44, which is raised to the power of 11 implicitly, we will also apply the same rule. (4d6)3=43×(d6)3(4d^6)^3 = 4^3 \times (d^6)^3
  2. Calculate 434^3: Calculate 434^3.\newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  3. Calculate (d6)3(d^6)^3: Calculate (d6)3(d^6)^3.(d6)3=d(6×3)=d18(d^6)^3 = d^{(6 \times 3)} = d^{18}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline(4d6)3=43×(d6)3=64×d18(4d^6)^3 = 4^3 \times (d^6)^3 = 64 \times d^{18}
  5. Write final expression: Write the final simplified expression.\newlineThe expression (4d6)3(4d^6)^3 simplifies to 64d1864d^{18}.

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