Simplify: `((81)/(16))^(-3/4)xx[((25)/9)^(-3/2)-:(5/2)^(-3)]`

Explanation

To simplify the expression \(\left(\frac{81}{16}\right)^{-\frac{3}{4}} \times \left[\left(\frac{25}{9}\right)^{-\frac{3}{2}} \div \left(\frac{5}{2}\right)^{-3}\right]\), we can follow these steps:

### Step 1: Rewrite the numbers in terms of their prime factors
- \(81 = 3^4\)
- \(16 = 2^4\)
- \(25 = 5^2\)
- \(9 = 3^2\)

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