Question

1. $(e^{2}k^{2})(e^{3}k)$

Explanation:

Step1: Use the product rule of exponents (\(a^m \cdot a^n = a^{m + n}\)) for like bases. First, group the terms with base \(e\) and terms with base \(k\).

\((e^{2}k^{2})(e^{3}k)=e^{2}\cdot e^{3}\cdot k^{2}\cdot k\)

Step2: Apply the product rule to the \(e\) terms and the \(k\) terms separately. For \(e\) terms: \(e^{2}\cdot e^{3}=e^{2 + 3}=e^{5}\). For \(k\) terms: \(k^{2}\cdot k = k^{2+1}=k^{3}\) (since \(k = k^{1}\)).

Step3: Multiply the results together.

\(e^{5}\cdot k^{3}=e^{5}k^{3}\)

Answer:

\(e^{5}k^{3}\)