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Simplify. Express your answer using a single exponent.\newline(9m6)2(9m^6)^2

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(9m6)2(9m^6)^2
  1. Apply Power Rule: Apply the power of a power rule to the expression (9m6)2(9m^6)^2. The power of a power rule states that when raising a power to another power, you multiply the exponents. For the coefficient 99, which is also a power (91)(9^1), we will square it. For the variable mm with an exponent of 66, we will multiply the exponents. (9m6)2=92×(m6)2(9m^6)^2 = 9^2 \times (m^6)^2
  2. Calculate 929^2: Calculate 929^2. \newline92=9×9=819^2 = 9 \times 9 = 81
  3. Calculate (m6)2(m^6)^2: Calculate (m6)2(m^6)^2.(m6)2=m(6×2)=m12(m^6)^2 = m^{(6 \times 2)} = m^{12}
  4. Combine Results: Combine the results from Step 22 and Step 33.\newline(9m6)2=81×m12(9m^6)^2 = 81 \times m^{12}
  5. Write Final Expression: Write the final simplified expression.\newlineThe final simplified expression is 81m1281m^{12}.

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