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Simplify. Express your answer using a single exponent.\newline(10d3)3(10d^3)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(10d3)3(10d^3)^3
  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(10d3)3=103×(d3)3(10d^3)^3 = 10^3 \times (d^3)^3
  2. Simplify 10310^3: Simplify 10310^3. \newline103=10×10×10=100010^3 = 10 \times 10 \times 10 = 1000
  3. Simplify (d3)3(d^3)^3: Simplify (d3)3(d^3)^3 by multiplying the exponents.\newlineWhen raising a power to another power, we multiply the exponents.\newline(d3)3=d(3×3)=d9(d^3)^3 = d^{(3 \times 3)} = d^9
  4. Combine Simplified Terms: Combine the simplified terms to write the final answer.\newline(10d3)3=103×d9=1000d9(10d^3)^3 = 10^3 \times d^9 = 1000d^9

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