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Simplify. Express your answer using a single exponent. \newline(12a9)2(12a^9)^2

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Powers of a power: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using a single exponent. \newline(12a9)2(12a^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 multiply the exponents, and when raising a number to a power, we simply calculate the number to that power.\newline(12a9)2=122×(a9)2(12a^9)^2 = 12^2 \times (a^9)^2
  2. Calculate 12212^2: Calculate 12212^2.\newline122=12×12=14412^2 = 12 \times 12 = 144
  3. Calculate (a9)2(a^9)^2: Calculate (a9)2(a^9)^2.\newlineWhen raising a power to another power, we multiply the exponents.\newline(a9)2=a(9×2)=a18(a^9)^2 = a^{(9 \times 2)} = a^{18}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline(12a9)2=144×a18(12a^9)^2 = 144 \times a^{18}

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