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Simplify. Express your answer using a single exponent.\newline(12q9)2(12q^9)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(12q9)2(12q^9)^2
  1. Apply Power Separately: Apply the power to both the coefficient and the variable separately.\newlineWhen raising a power to a power, we distribute the exponent to both the coefficient and the variable. \newline(12q9)2=(12)2×(q9)2(12q^9)^2 = (12)^2 \times (q^9)^2
  2. Calculate (12)2(12)^2: Calculate (12)2(12)^2.(12)2=12×12=144(12)^2 = 12 \times 12 = 144
  3. Calculate (q9)2(q^9)^2: Calculate (q9)2(q^9)^2.\newlineWhen raising a power to another power, we multiply the exponents.\newline(q9)2=q(9×2)=q18(q^9)^2 = q^{(9 \times 2)} = q^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(12q9)2=(12)2×(q9)2=144×q18(12q^9)^2 = (12)^2 \times (q^9)^2 = 144 \times q^{18}
  5. Write Final Expression: Write the final simplified expression.\newlineThe expression (12q9)2(12q^9)^2 simplifies to 144q18144q^{18}.

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