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Simplify. Express your answer using a single exponent.\newline(3p6)3(3p^6)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(3p6)3(3p^6)^3
  1. Apply Power Rule: Apply the power of a power rule to the expression (3p6)3(3p^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 coefficient 33 and the variable pp with its exponent. (3p6)3=33×(p6)3(3p^6)^3 = 3^3 \times (p^6)^3
  2. Calculate 333^3: Calculate the value of 333^3.\newline33=3×3×3=273^3 = 3 \times 3 \times 3 = 27
  3. Apply Power Rule to p6p^6: Apply the power of a power rule to (p6)3(p^6)^3.\newline(p6)3=p(6∗3)=p18(p^6)^3 = p^{(6*3)} = p^{18}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineThe simplified expression is 27×p18.27 \times p^{18}.

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