1. **State the problem:** Simplify the expression $$y = \sqrt[4]{x^5} - \frac{1}{\sqrt{x}}$$. 2. **Recall the rules:** - The fourth root can be written as a fractional exponent: $$\sqrt[4]{x^5} = x^{\frac{5}{4}}$$. - The square root can be written as a fractional exponent: $$\sqrt{x} = x^{\frac{1}{2}}$$. - Division by a root is the same as multiplying by the root with a negative exponent: $$\frac{1}{\sqrt{x}} = x^{-\frac{1}{2}}$$. 3. **Rewrite the expression using exponents:** $$y = x^{\frac{5}{4}} - x^{-\frac{1}{2}}$$ 4. **Final simplified form:** The expression is simplified as $$y = x^{\frac{5}{4}} - x^{-\frac{1}{2}}$$. This form is easier to work with for calculus or algebraic manipulation.