the quotient property of radicals requires the indices of the radicals to be the same. does this mean that…

Answer:

It is possible to write it as a single radical.

Explanation:

Step1: Rewrite radicals as exponents

We know that $\sqrt[4]{y^{3}}=y^{\frac{3}{4}}$ and $\sqrt{y}=y^{\frac{1}{2}}$.

Step2: Use exponent - division rule

When dividing terms with the same base ($y$ in this case), we subtract the exponents. So $\frac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}=y^{\frac{3}{4}-\frac{1}{2}}$.

Step3: Calculate the exponent

$\frac{3}{4}-\frac{1}{2}=\frac{3 - 2}{4}=\frac{1}{4}$. So $\frac{y^{\frac{3}{4}}}{y^{\frac{1}{2}}}=y^{\frac{1}{4}}=\sqrt[4]{y}$.