Find the value of \( (16)^{\frac{1}{4}} \times(125)^{\frac{1}{3}} \div(27)^{\frac{1}{3}} \)

To solve the expression \( (16)^{\frac{1}{4}} \times (125)^{\frac{1}{3}} \div (27)^{\frac{1}{3}} \), we first simplify each component. 1. **Calculate \( (16)^{\frac{1}{4}} \)**: \[ 16 = 2^4 \implies (16)^{\frac{1}{4}} = (2^4)^{\frac{1}{4}} = 2^{4 \times \frac{1}{4}} = 2^1 = 2 \] 2. **Calculate \( (125)^{\frac{1}{3}} \)**: \[ 125 = 5^3 \implies (125)^{\frac{1}{3}} = (5^3)^{\frac{1}{3}} = 5^{3 \times \frac{1}{3}} = 5^1 = 5 \] 3. **Calculate \( (27)^{\frac{1}{3}} \)**: \[ 27 = 3^3 \implies (27)^{\frac{1}{3}} = (3^3)^{\frac{1}{3}} = 3^{3 \times \frac{1}{3}} = 3^1 = 3 \] Now substituting these results into the original expression gives: \[ (16)^{\frac{1}{4}} \times (125)^{\frac{1}{3}} \div (27)^{\frac{1}{3}} = 2 \times 5 \div 3 \] Now we can calculate this: \[ 2 \times 5 = 10 \] Then, \[ 10 \div 3 = \frac{10}{3} \] Thus, the final result is \[ \boxed{\frac{10}{3}} \]