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Simplify. Express your answer using a single exponent.\newline(6n7)3(6n^7)^3

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(6n7)3(6n^7)^3
  1. Apply power rule: Apply the power rule to the expression (6n7)3(6n^7)^3. The power rule states that when raising a power to another power, you multiply the exponents. For the coefficient 66, which is raised to the power of 11 implicitly, it will be raised to the power of 33. For the variable nn with an exponent of 77, it will be raised to the power of 33 as well. (6n7)3=63×(n7)3(6n^7)^3 = 6^3 \times (n^7)^3
  2. Calculate 636^3: Calculate the value of 636^3.\newline63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216
  3. Multiply exponents: Multiply the exponents for n7n^7 raised to the power of 33. \newline(n7)3=n(7×3)=n21(n^7)^3 = n^{(7 \times 3)} = n^{21}
  4. Combine results: Combine the results from Step 22 and Step 33 to write the final simplified expression.\newline(6n7)3=63×n21=216n21(6n^7)^3 = 6^3 \times n^{21} = 216n^{21}

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