How can you use properties of exponents to simplify products and quotients of radicals?

You can use properties of exponents to simplify products and quotients of radicals by expressing the radicals in exponential form. For example, the square root of a number ( a ) can be written as ( a^{1/2} ). When multiplying radicals, you can add the exponents (e.g., ( \sqrt{a} \times \sqrt{b} = (a^{1/2} \times b^{1/2}) = (ab)^{1/2} )). For quotients, you subtract the exponents (e.g., ( \frac{\sqrt{a}}{\sqrt{b}} = \frac{a^{1/2}}{b^{1/2}} = \left(\frac{a}{b}\right)^{1/2} )).