Question

$$(\overline{a}^{\prime}+\overline{b}^{-1})^{-1}$$

Answer

$$1/(e^2*IM*o*v*r*l*n*a^prime+(e^2*IM*o*v*r*l*n)/b)$$

Solution


Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{(ov{e}^{2}rl\imath n{a}^{prime}+overl\imath ne{b}^{-1})}^{-1}\]
Regroup terms.
\[{({e}^{2}\imath ovrln{a}^{prime}+overl\imath ne{b}^{-1})}^{-1}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[{({e}^{2}\imath ovrln{a}^{prime}+ov{e}^{2}rl\imath n{b}^{-1})}^{-1}\]
Regroup terms.
\[{({e}^{2}\imath ovrln{a}^{prime}+{e}^{2}\imath ovrln{b}^{-1})}^{-1}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{{e}^{2}\imath ovrln{a}^{prime}+{e}^{2}\imath ovrln{b}^{-1}}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\frac{1}{{e}^{2}\imath ovrln{a}^{prime}+{e}^{2}\imath ovrln\times \frac{1}{b}}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{1}{{e}^{2}\imath ovrln{a}^{prime}+\frac{{e}^{2}\imath ovrln\times 1}{b}}\]
Simplify  \({e}^{2}\imath ovrln\times 1\)  to  \(ovrln{e}^{2}\imath \).
\[\frac{1}{{e}^{2}\imath ovrln{a}^{prime}+\frac{ovrln{e}^{2}\imath }{b}}\]
Regroup terms.
\[\frac{1}{{e}^{2}\imath ovrln{a}^{prime}+\frac{{e}^{2}\imath ovrln}{b}}\]