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Simplify. Express your answer using a single exponent.\newline(p2)−2(p^2)^{-2}

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Full solution

Q. Simplify. Express your answer using a single exponent.\newline(p2)−2(p^2)^{-2}
  1. Understand Exponent Rule: Understand the exponent rule for powers raised to powers.\newlineWhen we have an expression of the form (am)n(a^m)^n, we multiply the exponents mm and nn.
  2. Apply Rule to Given Expression: Apply the exponent rule to the given expression (p2)−2(p^2)^{-2}. We multiply the exponents 22 and −2-2. (p2)−2=p2⋅−2=p−4(p^2)^{-2} = p^{2 \cdot -2} = p^{-4}
  3. Express Final Answer: Express the final answer using a positive exponent.\newlineSince p−4p^{-4} means 1/p41/p^4, we can express the answer with a positive exponent as p−4p^{-4}.\newlineHowever, the question prompt asks for a positive exponent, so we need to keep the expression in the form of a reciprocal to comply with the prompt.

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