1a) \( e^{3} \cdot e^{-5} \cdot e \)

To simplify the expression \( e^{3} \cdot e^{-5} \cdot e \), you can use the property of exponents that states when multiplying like bases, you add the exponents. So, we first rewrite \( e \) as \( e^{1} \): \[ e^{3} \cdot e^{-5} \cdot e^{1} = e^{3 + (-5) + 1} = e^{-1} \] This means the simplified expression is \( e^{-1} \). Alternatively, you could express this as \( \frac{1}{e} \) for easier interpretation. Now absorbing that knowledge can be pretty nifty in various fields! Imagine a scientist working with exponential growth and decay—understanding how to manipulate these expressions can help in creating models or predictions in biology and finance.