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Simplify. Express your answer using a single exponent.\newline(12y9)2(12y^9)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(12y9)2(12y^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(12y9)2=(12)2×(y9)2(12y^9)^2 = (12)^2 \times (y^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 (y9)2(y^9)^2: Calculate (y9)2(y^9)^2.\newlineWhen raising a power to another power, we multiply the exponents.\newline(y9)2=y(9×2)=y18(y^9)^2 = y^{(9 \times 2)} = y^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(12y9)2=(12)2×(y9)2=144×y18(12y^9)^2 = (12)^2 \times (y^9)^2 = 144 \times y^{18}

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