((32x^frac (5)/(3)y^(2)/(3))^(1)/(5))((16x^-3y^2)^(1)/(2))

## Step 1: Simplify the Numerator### Apply the power of a power rule \((a^m)^n = a^{m \cdot n}\) to simplify the numerator. Calculate each component:- - - Thus, the simplified numerator is: ## Step 2: Simplify the Denominator### Apply the power of a power rule \((a^m)^n = a^{m \cdot n}\) to simplify the denominator. Calculate each component:- - - Thus, the simplified denominator is: ## Step 3: Divide the Simplified Expressions### Divide the simplified numerator by the simplified denominator. Calculate each component:- - - Thus, the final expression is: ## Step 4: Express with Positive Exponents### Rewrite the expression with positive exponents.