I. ` (x^(7//5) div 9) = 169 div x^(3//5)`
II. ` y^(1//4) xx y^(1//4) xx 7 = 273 div y^(1//2) `

Options

A. if`x gt y`
B. if `x ge y`
C. if `x lt y`
D. if `x le y`

Explanation

Let's solve the equations step by step.

### Part I: Solve for x

Given the equation:
\[ \frac{x^{7/5}}{9} = \frac{169}{x^{3/5}} \]

**Step 1: Cross-multiply to eliminate the fractions**
\[ x^{7/5} \cdot x^{3/5} = 169 \cdot 9 \]

**Hint:** When you have a fraction on both sides, you can cross-multiply to simplify the equation.

**Step 2: Combine the powers of x on the left side**
\[ x^{(7/5 + 3/5)} = 169 \cdot 9 \]
\[ x^{10/5} = 169 \cdot 9 \]
\[ x^2 = 169 \cdot 9 \]

**Hint:** When multiplying powers with the same base, you can add the exponents.

**Step 3: Calculate the right side**
\[ 169 \cdot 9 = 1521 \]
So, we have:
\[ x^2 = 1521 \]

**Hint:** Perform the multiplication carefully to ensure accuracy.

**Step 4: Take the square root of both sides**
\[ x = \pm \sqrt{1521} \]

**Hint:** Remember that taking the square root gives both positive and negative solutions.

**Step 5: Calculate the square root**
\[ \sqrt{1521} = 39 \]
Thus,
\[ x = \pm 39 \]

### Part II: Solve for y

Given the equation:
\[ y^{1/4} \cdot y^{1/4} \cdot 7 = \frac{273}{y^{1/2}} \]

**Step 1: Combine the powers of y on the left side**
\[ y^{1/2} \cdot 7 = \frac{273}{y^{1/2}} \]

**Hint:** When multiplying powers with the same base, you can add the exponents.

**Step 2: Cross-multiply to eliminate the fraction**
\[ 7y^{1/2} \cdot y^{1/2} = 273 \]
\[ 7y = 273 \]

**Hint:** Again, cross-multiplication helps to simplify the equation.

**Step 3: Solve for y**
\[ y = \frac{273}{7} \]
\[ y = 39 \]

### Conclusion

We found:
- \( x = \pm 39 \)
- \( y = 39 \)

### Final Relation
Since \( x \) can be both positive and negative, but \( y \) is positive, we can state:
\[ x \leq y \]