यदि `(x)/(y)=((3)/(2))^(2)div ((5)/(7))^(0)`, तब `((y)/(x))^(2)` का मान क्या होगा -

Options

A. `(81)/(16)`
B. `(4)/(9)`
C. `(16)/(9)`
D. `(16)/(81)`

Answer

To solve the problem, we start with the given equation:

\[ \frac{x}{y} = \left(\frac{3}{2}\right)^2 \div \left(\frac{5}{7}\right)^0 \]

### Step 1: Simplify the Right Side

First, we simplify the right side of the equation. We know that any number raised to the power of 0 is 1, so:

\[ \left(\frac{5}{7}\right)^0 = 1 \]

Thus, the equation simplifies to:

\[ \frac{x}{y} = \left(\frac{3}{2}\right)^2 \div 1 = \left(\frac{3}{2}\right)^2 \]

### Step 2: Calculate \(\left(\frac{3}{2}\right)^2\)

Now we calculate \(\left(\frac{3}{2}\right)^2\):

\[ \left(\frac{3}{2}\right)^2 = \frac{3^2}{2^2} = \frac{9}{4} \]

So, we have:

\[ \frac{x}{y} = \frac{9}{4} \]

### Step 3: Find \(\frac{y}{x}\)

To find \(\frac{y}{x}\), we take the reciprocal of \(\frac{x}{y}\):

\[ \frac{y}{x} = \frac{4}{9} \]

### Step 4: Calculate \(\left(\frac{y}{x}\right)^2\)

Now we need to find \(\left(\frac{y}{x}\right)^2\):

\[ \left(\frac{y}{x}\right)^2 = \left(\frac{4}{9}\right)^2 = \frac{4^2}{9^2} = \frac{16}{81} \]

### Final Answer

Thus, the value of \(\left(\frac{y}{x}\right)^2\) is:

\[ \frac{16}{81} \]

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