Answer:

Given expression: ((x y)^(2/3))/(√x y)

We need to simplify the given expression.

Step 1: Simplify the expression inside the bracket using exponent law.

(x y)^(2/3) = (x^(2/3) * y^(2/3))

Step 2: Substitute the simplified expression inside the bracket in the given expression.

((x y)^(2/3))/(√x y) = [(x^(2/3) * y^(2/3))/√(x y)]

Step 3: Simplify the denominator using exponent law.

√(x y) = (x y)^(1/2) = x^(1/2) * y^(1/2)

Step 4: Substitute the simplified denominator in the given expression.

[(x^(2/3) * y^(2/3))/√(x y)] = [(x^(2/3) * y^(2/3))/(x^(1/2) * y^(1/2))]

Step 5: Simplify the expression using exponent law.

[(x^(2/3) * y^(2/3))/(x^(1/2) * y^(1/2))] = x^(2/3-1/2) * y^(2/3-1/2)

= x^(1/6) * y^(1/6)

Therefore, the simplified value of ((x y)^(2/3))/(√x y) is x^(1/6) * y^(1/6).

Explanation:

The given expression is in the form of a fraction, where the numerator is raised to a fractional power and the denominator is a square root expression. We simplified the expression using exponent laws and simplified the denominator by converting it to an exponent expression. Finally, we combined the numerator and denominator using exponent laws to obtain the simplified expression.