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Simplify. Express your answer using a single exponent.\newline(6n9)3(6n^9)^3

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Q. Simplify. Express your answer using a single exponent.\newline(6n9)3(6n^9)^3
  1. Apply power rule: Apply the power of a power rule.\newlineThe power of a power rule states that when raising a power to another power, you multiply the exponents. In this case, we have (6n9)3(6n^9)^3, which means we need to raise both 66 and n9n^9 to the power of 33.\newline(6n9)3=63×(n9)3(6n^9)^3 = 6^3 \times (n^9)^3
  2. Calculate 636^3: Calculate 636^3.\newlineTo find 636^3, we multiply 66 by itself three times.\newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216
  3. Calculate (n9)3(n^9)^3: Calculate (n9)3(n^9)^3. Using the power of a power rule, we multiply the exponents 99 and 33. (n9)3=n(9×3)=n27(n^9)^3 = n^{(9 \times 3)} = n^{27}
  4. Combine results: Combine the results.\newlineNow we combine the results from Step 22 and Step 33 to get the final simplified expression.\newline(6n9)3=63×n27=216n27(6n^9)^3 = 6^3 \times n^{27} = 216n^{27}