1. **State the problem:** Write the logarithmic expressions as exponential expressions. 2. **Recall the logarithm to exponential conversion formula:** $$\log_b a = c \iff b^c = a$$ 3. **Problem 18:** Given: $$18\ \ln\left(\frac{\sqrt[3]{x^2}}{w+z}\right) = \ln \sqrt[3]{x^2} - \ln(w+z)$$ Rewrite the logarithms: $$\sqrt[3]{x^2} = x^{\frac{2}{3}}$$ So, $$18 = \frac{2}{3} \ln x - \ln(w+z)$$ Express as a single logarithm: $$18 = \ln x^{\frac{2}{3}} - \ln(w+z) = \ln \left(\frac{x^{\frac{2}{3}}}{w+z}\right)$$ 4. **Convert to exponential form:** Since the natural logarithm base is $e$, we have $$e^{18} = \frac{x^{\frac{2}{3}}}{w+z}$$ 5. **Final exponential expression for problem 18:** $$\boxed{e^{18} = \frac{x^{\frac{2}{3}}}{w+z}}$$ --- 6. **Problem 19:** Given: $$\log_2 \sqrt{\frac{4x}{yz^3}}$$ Rewrite the square root as a power of $\frac{1}{2}$: $$\log_2 \left(\frac{4x}{yz^3}\right)^{\frac{1}{2}}$$ 7. **Convert to exponential form:** Using the formula $\log_b a = c \iff b^c = a$, let $$c = \log_2 \left(\frac{4x}{yz^3}\right)^{\frac{1}{2}}$$ Then $$2^c = \left(\frac{4x}{yz^3}\right)^{\frac{1}{2}}$$ 8. **Final exponential expression for problem 19:** $$\boxed{2^{\log_2 \sqrt{\frac{4x}{yz^3}}} = \sqrt{\frac{4x}{yz^3}}}$$ **Summary:** - Problem 18 exponential form: $$e^{18} = \frac{x^{\frac{2}{3}}}{w+z}$$ - Problem 19 exponential form: $$2^{\log_2 \sqrt{\frac{4x}{yz^3}}} = \sqrt{\frac{4x}{yz^3}}$$