Respuesta :

Given:

The expression is,

[tex]e^{6-8\ln (x)+\ln (y)}[/tex]

Explanation:

Simplify the expression by using logathimic properties.

[tex]\begin{gathered} e^{6-8\ln (x)+\ln (y)_{}}=e^{6-\ln (x^8)+\ln (y)} \\ =e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)} \end{gathered}[/tex]

Simplify further.

[tex]\begin{gathered} e^6\cdot e^{-\ln (x^8)}\cdot e^{\ln (y)}=e^6\cdot\frac{1}{e^{\ln(x^8)}}\cdot e^{\ln (y)} \\ =e^6\cdot\frac{1}{x^8}\cdot y \\ =\frac{e^6y}{x^8} \end{gathered}[/tex]

So answer is,

[tex]\frac{e^6y}{x^8}[/tex]

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