Verified Answer :

Divide both sides by 2³. Remember, when dividing exponent terms with the same base, you subtract the exponents. 

You're then left with \(2^{n}\) = \(2^{6}\)

Therefore, n = 6

Panoyin

\(2^{3} + 2^{n} = 2^{9}\)
\(8 + 2^{n} = 512\)
\(- 8\)    \(- 8\)
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\(2^{n}) = 504\)
\(ln(2^{x}) = ln(504)\)
\(xln(2) = ln(504)\)
\(x = \frac{ln(504)}{ln(2)}\)