1. **State the problem:** Determine if the equation $$\sqrt[18]{5} = \sqrt[6]{5} \times \sqrt[3]{5}$$ is true or false. 2. **Recall the rule for roots:** The $n$th root of a number $a$ can be written as an exponent: $$\sqrt[n]{a} = a^{\frac{1}{n}}$$. 3. **Rewrite each term using exponents:** $$\sqrt[18]{5} = 5^{\frac{1}{18}}$$ $$\sqrt[6]{5} = 5^{\frac{1}{6}}$$ $$\sqrt[3]{5} = 5^{\frac{1}{3}}$$ 4. **Rewrite the right side of the equation:** $$\sqrt[6]{5} \times \sqrt[3]{5} = 5^{\frac{1}{6}} \times 5^{\frac{1}{3}}$$ 5. **Use the property of exponents:** When multiplying with the same base, add the exponents: $$5^{\frac{1}{6}} \times 5^{\frac{1}{3}} = 5^{\frac{1}{6} + \frac{1}{3}}$$ 6. **Add the exponents:** $$\frac{1}{6} + \frac{1}{3} = \frac{1}{6} + \frac{2}{6} = \frac{3}{6} = \frac{1}{2}$$ 7. **So the right side becomes:** $$5^{\frac{1}{2}} = \sqrt{5}$$ 8. **Compare both sides:** Left side: $$5^{\frac{1}{18}}$$ Right side: $$5^{\frac{1}{2}}$$ Since $$\frac{1}{18} \neq \frac{1}{2}$$, the two sides are not equal. **Final answer:** The equation $$\sqrt[18]{5} = \sqrt[6]{5} \times \sqrt[3]{5}$$ is **False**.