Question

1. \\(\frac{e^{3}}{r^{5}}\left(\frac{e^{2}}{4r} + \frac{r^{9}}{k}\

ight)\\)

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c)=ab+ac\) where \(a = \frac{e^{3}}{r^{5}}\), \(b=\frac{e^{2}}{4r}\) and \(c = \frac{r^{9}}{k}\). So we get \(\frac{e^{3}}{r^{5}}\times\frac{e^{2}}{4r}+\frac{e^{3}}{r^{5}}\times\frac{r^{9}}{k}\)

Step2: Simplify exponents for \(e\) and \(r\)

For the first term, using \(a^{m}\times a^{n}=a^{m + n}\) for \(e\) and \(a^{m}\div a^{n}=a^{m - n}\) for \(r\): \(\frac{e^{3+2}}{4r^{5 + 1}}=\frac{e^{5}}{4r^{6}}\)
For the second term, using \(a^{m}\times a^{n}=a^{m + n}\) for \(r\): \(\frac{e^{3}r^{9-5}}{k}=\frac{e^{3}r^{4}}{k}\)

Step3: Combine the terms

The simplified expression is \(\frac{e^{5}}{4r^{6}}+\frac{e^{3}r^{4}}{k}\)

Answer:

\(\frac{e^{5}}{4r^{6}}+\frac{e^{3}r^{4}}{k}\)