Use Power Rule: \(\ln{({x}^{y})}=y\ln{x}\).
\[\begin{aligned}&{0}^{-12}\times \frac{w}{{m}^{2}}\\&\log_{_5}{125}+\frac{1}{2}\ln{e}\end{aligned}\]
Use Rule of e: \(\ln{e}=1\).
\[\begin{aligned}&{0}^{-12}\times \frac{w}{{m}^{2}}\\&\log_{_5}{125}+\frac{1}{2}\times 1\end{aligned}\]
Use Negative Power Rule: \({x}^{-a}=\frac{1}{{x}^{a}}\).
\[\begin{aligned}&\frac{1}{{0}^{12}}\times \frac{w}{{m}^{2}}\\&\log_{_5}{125}+\frac{1}{2}\times 1\end{aligned}\]
Simplify \({0}^{12}\) to \(0\).
\[\begin{aligned}&\frac{1}{0}\times \frac{w}{{m}^{2}}\\&\log_{_5}{125}+\frac{1}{2}\times 1\end{aligned}\]
Simplify \(\frac{1}{0}\) to \(\infty \).
\[\begin{aligned}&\infty \times \frac{w}{{m}^{2}}\\&\log_{_5}{125}+\frac{1}{2}\times 1\end{aligned}\]
Simplify \(\frac{1}{2}\times 1\) to \(\frac{1}{2}\).
\[\begin{aligned}&\infty \times \frac{w}{{m}^{2}}\\&\log_{_5}{125}+\frac{1}{2}\end{aligned}\]
INF*w/m^2;log(_5,125)+1/2
