https://file.aiquickdraw.com/mathbot/file/17337287560030r8ebg7h.jpg

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!  

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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.

Simplify the expression \(\left( \frac{3}{4x} y^{\frac{1}{2}} \right)^{\frac{1}{4}}\) using only positive exponents.

Learn how to simplify the expression \(\left( \frac{3}{4x} y^{\frac{1}{2}} \right)^{\frac{1}{4}}\) using only positive exponents. This solution covers key exponent rules, including fractional exponents and the simplification of algebraic expressions. Suitable for students in Grades 9-11.

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