Jse the properties of logarithms to write the following expression as a single term that doesn't contain a logaritl $$ e^{8-5 \ln (x)+\ln (y)} $$

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To simplify the expression $$ e^{8-5 \ln (x)+\ln (y)} $$ using the properties of logarithms, we can follow these steps:

1. **Separate the exponent**: Rewrite the exponent as a sum of terms:
   $$
   e^{8} \cdot e^{-5 \ln (x)} \cdot e^{\ln (y)}
   $$

2. **Apply the properties of exponents and logarithms**:
   - Recall that $$ e^{\ln(a)} = a $$ and $$ e^{k \ln(a)} = a^k $$.
   - Therefore, we can rewrite $$ e^{-5 \ln (x)} $$ as $$ x^{-5} $$ and $$ e^{\ln (y)} $$ as $$ y $$.

3. **Combine the terms**:
   $$
   e^{8} \cdot x^{-5} \cdot y
   $$

Now, let's express this in a single term:
$$
\frac{e^{8} \cdot y}{x^{5}}
$$

Thus, the expression $$ e^{8-5 \ln (x)+\ln (y)} $$ can be written as:
$$
\frac{e^{8} y}{x^{5}}
$$
The expression simplifies to $$ \frac{e^{8} y}{x^{5}} $$.

Jse the properties of logarithms to write the following expression as a single term that doesn’t contain a logaritl

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