Question

simplify the expression \\(\frac{48e^6}{8e^2}\\). (1 point)

Explanation:

Step1: Simplify the coefficient

First, simplify the coefficient part \(\frac{48}{8}\). Since \(48\div8 = 6\), the coefficient simplifies to 6.

Step2: Simplify the exponential part

Next, simplify the exponential part \(\frac{e^{6}}{e^{2}}\). Using the rule of exponents \(\frac{a^{m}}{a^{n}}=a^{m - n}\), we have \(e^{6-2}=e^{4}\).

Step3: Combine the results

Now, combine the simplified coefficient and the simplified exponential part. So, \(\frac{48e^{6}}{8e^{2}}=6e^{4}\).

Answer:

The value in the box is \(6\), so the simplified expression is \(6e^{4}\).