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Simplify. Express your answer using positive exponents.\newlinep−5×p−4×p7p^{-5} \times p^{-4} \times p^{7}

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Full solution

Q. Simplify. Express your answer using positive exponents.\newlinep−5×p−4×p7p^{-5} \times p^{-4} \times p^{7}
  1. Identify needed operation: p−5×p−4×p7p^{-5} \times p^{-4} \times p^{7}\newlineWhat operation is needed for the exponents −5-5, −4-4, and 77?\newlineWhen we multiply powers with the same base, we add the exponents.
  2. Combine exponents: p−5×p−4×p7p^{-5} \times p^{-4} \times p^{7}\newlineRewrite this expression as a single power of pp.\newlinep−5×p−4×p7p^{-5} \times p^{-4} \times p^{7} \newline= p(−5+(−4)+7)p^{(-5 + (-4) + 7)}\newline= p(−5−4+7)p^{(-5 - 4 + 7)}\newline= p(−9+7)p^{(-9 + 7)}\newline= p−2p^{-2}
  3. Express in positive form: p−2p^{-2}\newlineExpress the answer using positive exponents.\newlineSince p−2p^{-2} is the same as 1/p21/p^2, we can rewrite the expression with a positive exponent.

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