Simplify the expression: \( x^{2/3} \cdot y^{-1/6} \cdot x^{-1/9} \)

To simplify the expression \( x^{2/3} \cdot y^{-1/6} \cdot x^{-1/9} \), we start by combining the terms involving \( x \). 1. Combine the \( x \) terms: \[ x^{2/3} \cdot x^{-1/9} = x^{2/3 - 1/9} \] To perform the subtraction, we need a common denominator. The least common multiple of 3 and 9 is 9, so we convert: \[ 2/3 = 6/9 \] Now we can subtract: \[ 6/9 - 1/9 = 5/9 \] So, we have: \[ x^{2/3} \cdot x^{-1/9} = x^{5/9} \] 2. Now, include the term with \( y \): \[ x^{5/9} \cdot y^{-1/6} \] Thus, the simplified expression is: \[ \frac{x^{5/9}}{y^{1/6}} \]