Question

1. simplify the expression.

$e^x \cdot e^{-6x} \cdot e^8 = \square$

Explanation:

Step1: Recall the exponent rule for multiplication

When multiplying exponential expressions with the same base, we add the exponents. The rule is \(a^m \cdot a^n = a^{m + n}\), where \(a = e\) in this case.
So for \(e^{x} \cdot e^{-6x} \cdot e^{8}\), we add the exponents of \(e\).

Step2: Add the exponents

The exponents are \(x\), \(-6x\), and \(8\). Adding them together: \(x + (-6x) + 8 = -5x + 8\).
So the simplified expression is \(e^{-5x + 8}\) (or it can also be written as \(e^{8 - 5x}\)).

Answer:

\(e^{8 - 5x}\) (or \(e^{-5x + 8}\))