Let us find out the values : 4^{1/3}\times [2^{1/3} \times 3^{1/2}] \div 9^{1/4}

4^\frac{1}{3}× [2^\frac{1}{3} × 3^\frac{1}{2}] \div 9^\frac{1}{4}

= \frac{4^\frac{1}{3}\times [2^\frac{1}{3} \times 3^\frac{1}{2}]}{9^\frac{1}{4}}

= \frac{\big\{(2)^2\big\}^\frac{1}{3}\times 2^\frac{1}{3} \times 3^\frac{1}{2}}{3^{2 \times \frac{1}{4}} }

= \frac{2^{2 \times \frac{1}{3}} \times 2^\frac{1}{3} \times 3^{1/2} }{{3^{2 \times \frac{1}{4}} }}

= \frac{2^{\frac{2}{3}} \times 2^\frac{1}{3} \times 3^\frac{1}{2}}{3^{\frac{1}{2}}}

= \frac{2^{ \frac{2}{3} + \frac{1}{3} } \times 1}{1}

= 2^{\frac{2+1}{3} }

= 2^\frac{3}{3} = 2¹ = 2