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In the following equation, what is the value of cc?\newline8c=(8−4)58^c = (8^{-4})^5\newlinec=c = ____

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Full solution

Q. In the following equation, what is the value of cc?\newline8c=(8−4)58^c = (8^{-4})^5\newlinec=c = ____
  1. Identify and Simplify: Identify the equation and simplify the right-hand side using the power of a power rule.\newlineCalculation: (8−4)5=8(−4∗5)=8−20(8^{-4})^5 = 8^{(-4*5)} = 8^{-20}.
  2. Set Equal and Solve: Set the simplified equation equal to the left-hand side and solve for cc.\newlineCalculation: 8c=8−208^c = 8^{-20}, so c=−20c = -20.

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