Simplify :
`[(125)/(27)xx((9)/(25))^3]div((3)/(5))^2`

Answer

To simplify the expression \(\frac{125}{27} \times \left(\frac{9}{25}\right)^3 \div \left(\frac{3}{5}\right)^2\), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression:
\[ \frac{125}{27} \times \left(\frac{9}{25}\right)^3 \div \left(\frac{3}{5}\right)^2 \]
This can be rewritten as:
\[ \frac{125}{27} \times \left(\frac{9}{25}\right)^3 \times \left(\frac{5}{3}\right)^2 \]

### Step 2: Calculate \(\left(\frac{9}{25}\right)^3\)
Next, we calculate \(\left(\frac{9}{25}\right)^3\):
\[ \left(\frac{9}{25}\right)^3 = \frac{9^3}{25^3} = \frac{729}{15625} \]

### Step 3: Calculate \(\left(\frac{5}{3}\right)^2\)
Now we calculate \(\left(\frac{5}{3}\right)^2\):
\[ \left(\frac{5}{3}\right)^2 = \frac{5^2}{3^2} = \frac{25}{9} \]

### Step 4: Substitute back into the expression
Now we substitute these values back into the expression:
\[ \frac{125}{27} \times \frac{729}{15625} \times \frac{25}{9} \]

### Step 5: Combine the fractions
We can combine the fractions:
\[ = \frac{125 \times 729 \times 25}{27 \times 15625 \times 9} \]

### Step 6: Simplify the numerator and denominator
Now we simplify the numerator and denominator:
- The numerator: \(125 \times 25 = 3125\)
- The denominator: \(27 \times 9 = 243\) and \(15625 = 125^3\)

So we have:
\[ = \frac{3125 \times 729}{243 \times 15625} \]

### Step 7: Factor and cancel common terms
Now we can factor and cancel common terms. We know:
- \(3125 = 5^5\)
- \(729 = 3^6\)
- \(243 = 3^5\)
- \(15625 = 5^6\)

This gives us:
\[ = \frac{5^5 \times 3^6}{3^5 \times 5^6} \]

### Step 8: Cancel common bases
Now we can cancel the common bases:
\[ = \frac{3^{6-5}}{5^{6-5}} = \frac{3^1}{5^1} = \frac{3}{5} \]

### Final Answer
Thus, the simplified expression is:
\[ \frac{3}{5} \]