In calculus it is frequently important to write an expression in the form \( c x^{n} \), where \( c \) is a constant and \( n \) is a rational number. Write the following expression in this form. \[ \sqrt{x} \cdot \sqrt[4]{x} \] SUBMIT ANSWER

To rewrite the expression \( \sqrt{x} \cdot \sqrt[4]{x} \) in the form \( c x^n \), we start by expressing each square root in terms of rational exponents. The square root \( \sqrt{x} \) can be written as \( x^{1/2} \) and the fourth root \( \sqrt[4]{x} \) can be expressed as \( x^{1/4} \). Now we can multiply these two together: \[ \sqrt{x} \cdot \sqrt[4]{x} = x^{1/2} \cdot x^{1/4} = x^{1/2 + 1/4} = x^{2/4 + 1/4} = x^{3/4}. \] So, in the required form, we have: \[ x^{3/4} \text{ (where } c = 1 \text{ and } n = \frac{3}{4}). \]