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In the following equation, what is the value of nn?\newline8n=8−3×878^n = 8^{-3} \times 8^7\newlinen=n = ____

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Full solution

Q. In the following equation, what is the value of nn?\newline8n=8−3×878^n = 8^{-3} \times 8^7\newlinen=n = ____
  1. Identify Bases and Simplify: Identify the bases and simplify the right-hand side using the properties of exponents. \newline8n=8(−3+7)8^n = 8^{(-3 + 7)}\newlineCalculation: −3+7=4-3 + 7 = 4
  2. Set Equal and Solve: Set the simplified expression equal to the left-hand side and solve for nn.8n=848^n = 8^4Therefore, n=4n = 4

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