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Simplify. Express your answer using a single exponent.\newline(3u9)3(3u^{9})^{3}

Full solution

Q. Simplify. Express your answer using a single exponent.\newline(3u9)3(3u^{9})^{3}
  1. Apply Power Rule: Apply the power of a power rule to the expression (3u9)3(3u^9)^3. The power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have an exponent of 99 being raised to the power of 33. (3u9)3=33×(u9)3(3u^9)^3 = 3^3 \times (u^9)^3
  2. Calculate 333^3: Calculate the value of 333^3.\newline333^3 is 33 multiplied by itself 33 times.\newline33=3×3×3=273^3 = 3 \times 3 \times 3 = 27
  3. Apply Power Rule: Apply the power of a power rule to (u9)3(u^9)^3. We multiply the exponents 99 and 33 to get the new exponent for uu. (u9)3=u(9×3)=u27(u^9)^3 = u^{(9 \times 3)} = u^{27}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newlineWe have calculated 333^3 to be 2727 and (u9)3(u^9)^3 to be u27u^{27}. Now we combine these results to get the final simplified expression.\newline(3u9)3=27u27(3u^9)^3 = 27u^{27}