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Simplify. Express your answer using a single exponent.\newline(6s6)3(6s^6)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(6s6)3(6s^6)^3
  1. Apply Power Rule: Apply the power of a power rule to the expression (6s6)3(6s^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 coefficient and the variable with its exponent. (6s6)3=63×(s6)3(6s^6)^3 = 6^3 \times (s^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 ss with its exponent.(s6)3=s(6∗3)=s18(s^6)^3 = s^{(6*3)} = s^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33 to write the final simplified expression.\newline(6s6)3=63×(s6)3=216×s18(6s^6)^3 = 6^3 \times (s^6)^3 = 216 \times s^{18}
  5. Write Final Answer: Write the final answer in the form of a single exponent as required by the question prompt.\newlineThe final simplified expression is 216s18216s^{18}.

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