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Simplify. Express your answer using a single exponent.\newline(a−4)6(a^{-4})^{6}

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(a−4)6(a^{-4})^{6}
  1. Identify Operation: Identify the operation needed for the exponents.\newlineWhen raising a power to a power, we multiply the exponents.
  2. Apply Exponent Rule: Apply the exponent rule (am)n=am∗n(a^m)^n = a^{m*n}.\newlineHere, we have (a−4)6(a^{-4})^6, so we multiply the exponents −4-4 and 66.\newline(a−4)6=a(−4∗6)(a^{-4})^6 = a^{(-4*6)}
  3. Perform Multiplication: Perform the multiplication of the exponents. a(−4×6)=a−24a^{(-4\times 6)} = a^{-24}
  4. Express Final Answer: Express the final answer using a single exponent.\newlineThe simplified expression is a−24a^{-24}.

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