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Simplify. Express your answer using a single exponent.\newline(6w2)3(6w^2)^3

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Powers of a power: variable basesright chevron icon

Full solution

Q. Simplify. Express your answer using a single exponent.\newline(6w2)3(6w^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(6w2)3=63×(w2)3(6w^2)^3 = 6^3 \times (w^2)^3
  2. Calculate Coefficient Cube: Calculate the cube of the coefficient 66. \newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216
  3. Multiply Exponents: Multiply the exponents for the variable ww.(w2)3=w(2×3)=w6(w^2)^3 = w^{(2 \times 3)} = w^6
  4. Combine Results: Combine the results from Step 22 and Step 33 to write the final simplified expression.\newline(6w2)3=216×w6=216w6(6w^2)^3 = 216 \times w^6 = 216w^6

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