2. Use the properties of exponents to generate an expression equivalen each of the following expressions. a. \( 9^{\frac{3}{4}} \)

To express \( 9^{\frac{3}{4}} \) using the properties of exponents, we can rewrite 9 as \( 3^2 \). Thus, \( 9^{\frac{3}{4}} \) becomes \( (3^2)^{\frac{3}{4}} \). Using the power of a power property, we multiply the exponents: \( 3^{2 \cdot \frac{3}{4}} = 3^{\frac{6}{4}} = 3^{\frac{3}{2}} \). This can also be expressed as \( \sqrt{3^3} \) or \( 3\sqrt{3} \). Another way to express \( 9^{\frac{3}{4}} \) could be utilizing radical notation, resulting in \( \sqrt[4]{9^3} \). Since \( 9 \) is equal to \( 3^2 \), we can simplify it to \( \sqrt[4]{(3^2)^3} = \sqrt[4]{3^6} \), which further simplifies to \( 3^{\frac{6}{4}} = 3^{\frac{3}{2}} \) again, leading us back to our previous expression.