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Simplify. Express your answer using a single exponent.\newline(6q2)3(6q^2)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(6q2)3(6q^2)^3
  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 coefficient to a power, we simply calculate the power of the number.\newline(6q2)3=63×(q2)3(6q^2)^3 = 6^3 \times (q^2)^3
  2. Calculate Coefficient Power: Calculate the power of the coefficient 636^3. \newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216
  3. Calculate Variable Power: Calculate the power of the variable (q2)3(q^2)^3. When raising a power to another power, we multiply the exponents. (q2)3=q(2×3)=q6(q^2)^3 = q^{(2 \times 3)} = q^6
  4. Combine Results: Combine the results from Step 22 and Step 33 to write the expression in simplest form.\newline(6q2)3=63×(q2)3=216×q6=216q6(6q^2)^3 = 6^3 \times (q^2)^3 = 216 \times q^6 = 216q^6

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