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Simplify. Express your answer using a single exponent.\newline(12v5)2(12v^5)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(12v5)2(12v^5)^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(12v5)2=(12)2×(v5)2(12v^5)^2 = (12)^2 \times (v^5)^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 (v5)2(v^5)^2: Calculate (v5)2(v^5)^2.\newlineWhen raising a power to another power, we multiply the exponents.\newline(v5)2=v(5×2)=v10(v^5)^2 = v^{(5 \times 2)} = v^{10}
  4. \newline \newline
  5. Write Final Expression: Write the final simplified expression.\newline(12v5)2=144v10(12v^5)^2 = 144v^{10}

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