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Simplify. Express your answer using a single exponent.\newline(12r6)2(12r^6)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(12r6)2(12r^6)^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(12r6)2=122×(r6)2(12r^6)^2 = 12^2 \times (r^6)^2
  2. Calculate 12212^2: Calculate 12212^2.\newline122=12×12=14412^2 = 12 \times 12 = 144
  3. Calculate (r6)2(r^6)^2: Calculate (r6)2(r^6)^2.\newlineWhen raising a power to another power, we multiply the exponents.\newline(r6)2=r(6×2)=r12(r^6)^2 = r^{(6 \times 2)} = r^{12}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(12r6)2=144×r12(12r^6)^2 = 144 \times r^{12}

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