Answer
(a) $e^{\ln7.2}=7.2$
(b) $e^{-\ln x^2}=\frac{1}{x^2}$
(c) $e^{\ln x-\ln y}=\frac{x}{y}$
Work Step by Step
This whole exercise is based on this property: $$e^{\ln x}=x\hspace{1cm}x\gt0$$
(a) $$e^{\ln7.2}$$
Here, $7.2\gt0$, so $$e^{\ln7.2}=7.2$$
(b) $$e^{-\ln x^2}$$
- Apply Reciprocal Rule for $-\ln x^2$: $-\ln x^2=\ln\frac{1}{x^2}$
$$e^{-\ln x^2}=e^{\ln\frac{1}{x^2}}=\frac{1}{x^2}$$
(c) $$e^{\ln x-\ln y}$$
- Apply Quotient Rule here: $\ln x-\ln y =\ln\frac{x}{y}$
$$e^{\ln x-\ln y}=e^{\ln\frac{x}{y}}=\frac{x}{y}$$
