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Simplify. Express your answer using a single exponent.\newline(4d9)3(4d^9)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(4d9)3(4d^9)^3
  1. Apply Power Rule: Apply the power to a power rule.\newlineWhen raising a power to another power, we multiply the exponents. We also raise the numerical coefficient to the power of 33.\newline(4d9)3=43×(d9)3(4d^9)^3 = 4^3 \times (d^9)^3
  2. Calculate 434^3: Calculate 434^3.\newline43=4×4×4=644^3 = 4 \times 4 \times 4 = 64
  3. Calculate (d9)3(d^9)^3: Calculate (d9)3(d^9)^3.(d9)3=d(9×3)=d27(d^9)^3 = d^{(9 \times 3)} = d^{27}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(4d9)3=43×(d9)3=64×d27(4d^9)^3 = 4^3 \times (d^9)^3 = 64 \times d^{27}
  5. Write Final Expression: Write the final simplified expression.\newlineThe expression (4d9)3(4d^9)^3 simplifies to 64d2764d^{27}.

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