\( \frac{\sqrt[4]{y^{3}}}{\sqrt{y}} \) as a single radical? Explain.

To simplify \( \frac{\sqrt[4]{y^{3}}}{\sqrt{y}} \) as a single radical, start by expressing both radicals with exponents: - The fourth root of \( y^3 \) can be represented as \( y^{3/4} \). - The square root of \( y \) can be expressed as \( y^{1/2} \). Now, rewrite the expression: \[ \frac{y^{3/4}}{y^{1/2}} = y^{3/4 - 1/2} \] To combine the exponents, convert \( 1/2 \) to a fraction with the same denominator: \[ 1/2 = 2/4 \] Now, we have: \[ 3/4 - 2/4 = 1/4 \] Thus, \[ \frac{\sqrt[4]{y^{3}}}{\sqrt{y}} = y^{1/4} \] Finally, convert back to radical form: \[ \sqrt[4]{y} \] So, the expression simplifies to \( \sqrt[4]{y} \).