Simplify the expression $(y^{\frac{3}{4}})^{\frac{1}{2}}$.

1. Problem Description

Simplify the expression $(y^{\frac{3}{4}})^{\frac{1}{2}}$.

2. Solution Steps

We are asked to simplify the expression $(y^{\frac{3}{4}})^{\frac{1}{2}}$.

We can use the power of a power rule which states that $(a^m)^n = a^{m \cdot n}$.

Applying the power of a power rule:

$(y^{\frac{3}{4}})^{\frac{1}{2}} = y^{\frac{3}{4} \cdot \frac{1}{2}} = y^{\frac{3 \cdot 1}{4 \cdot 2}} = y^{\frac{3}{8}}$.

3. Final Answer

$y^{\frac{3}{8}}$