Final answer:
The expression x^(2/6) * y^(3/6) simplifies to x^(1/3) * y^(1/2), which represents the cube root of x multiplied by the square root of y.
Step-by-step explanation:
To express the value of x^(2/6) * y^(3/6) with fractional exponents instead of radicals, we need to simplify the exponents first. The exponents 2/6 and 3/6 can be reduced to 1/3 and 1/2, respectively. Therefore, the expression becomes x^(1/3) * y^(1/2). This means we are looking at the cube root of x multiplied by the square root of y.
Remember that when you are multiplying terms with the same base, you can add the exponents if they are in exponent form. However, since our bases here are different (x and y), we cannot simplify this expression any further by combining the bases. The expression x^(1/3) * y^(1/2) is already in its simplest form with fractional exponents.