The problem asks to simplify an expression using only positive exponents. From the image, the expression appears to be:

$\left( \frac{3}{4x} y^{\frac{1}{2}} \right)^{\frac{1}{4}}$

Let’s work step by step:

Step 1: Apply the power rule

The expression can be simplified using the rule $(a^m)^n = a^{m \cdot n}$, applying the $\frac{1}{4}$ power to each term inside the parentheses.

1. For $\frac{3}{4x}$:

   • $3^{\frac{1}{4}}$ stays as it is.
   • $(4x)^{\frac{1}{4}}$ becomes $4^{\frac{1}{4}} \cdot x^{-\frac{1}{4}}$ (since $x$ is in the denominator, its exponent is negative).

2. For $y^{\frac{1}{2}}$:

   • Applying $\frac{1}{4}$, the power becomes $y^{\frac{1}{2} \cdot \frac{1}{4}} = y^{\frac{1}{8}}$.

Thus, the expression becomes:

$\frac{3^{\frac{1}{4}} \cdot y^{\frac{1}{8}}}{4^{\frac{1}{4}} \cdot x^{\frac{1}{4}}}.$

Step 2: Rewrite using positive exponents

All exponents are positive. The simplified expression is:

$\frac{3^{\frac{1}{4}} \cdot y^{\frac{1}{8}}}{4^{\frac{1}{4}} \cdot x^{\frac{1}{4}}}.$

If you'd like further steps, such as numerical approximations or more formatting adjustments, let me know!

Would you like more details about these steps? Here are 5 related questions for practice:

1. Simplify $\left( \frac{2}{3x} z^2 \right)^{\frac{1}{2}}$ using positive exponents.
2. How do you simplify $(a^{m}/b^{n})^{p}$ generally?
3. What is the cube root of $\frac{5x}{8y}$ in terms of fractional exponents?
4. What is the general rule for handling negative exponents in a fraction?
5. Convert $2^{-\frac{3}{4}}$ into a fraction and simplify.

Tip: Always apply powers to both the numerator and denominator separately to avoid mistakes when simplifying fractional expressions.