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In the following equation, what is the value of $n$ ? $\newline$ $8^n = 8^{-3} \times 8^7$ $\newline$ $n =$ ____

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Solve equations with variable exponents

Full solution

Q. In the following equation, what is the value of

n

?

\newline

8^n = 8^{-3} \times 8^7

\newline

n =

____

Identify Bases and Simplify: Identify the bases and simplify the right-hand side using the properties of exponents. $\newline$ $8^n = 8^{(-3 + 7)}$ $\newline$ Calculation: $-3 + 7 = 4$
Set Equal and Solve: Set the simplified expression equal to the left-hand side and solve for $n$ . $8^n = 8^4$ Therefore, $n = 4$

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