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Simplify. Express your answer using a single exponent.\newline(6q6)3(6q^6)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(6q6)3(6q^6)^3
  1. Apply Power Rule: Apply the power of a power rule to the expression (6q6)3(6q^6)^3. The power of a power rule states that (am)n=am∗n(a^m)^n = a^{m*n}. We will apply this rule to both the numerical part and the variable part of the expression. (6q6)3=63×(q6)3(6q^6)^3 = 6^3 \times (q^6)^3
  2. Calculate Cube of 66: Calculate the cube of 66, which is 636^3. \newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216
  3. Apply Power Rule to Variable: Apply the power of a power rule to the variable part (q6)3(q^6)^3.(q6)3=q(6∗3)=q18(q^6)^3 = q^{(6*3)} = q^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33 to write the final simplified expression.\newline(6q6)3=63×q18=216q18(6q^6)^3 = 6^3 \times q^{18} = 216q^{18}

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