Final answer:
The expression (16x^-2/3)y)^1/3 can be written in radical form as 2x^{-2/9}√[3]{y}, by translating the fractional exponents into cube roots and knowing that 16 is a perfect cube equal to 2^4.
Step-by-step explanation:
The question involves writing the expression (16x^-2/3)y)^1/3 in radical form. To do this, we raise each expression inside the parentheses to the power of 1/3. Remember, when we raise to a fractional power, the numerator of the fraction indicates the power and the denominator indicates the root. Hence, the cube root of an expression raised to the power of 1 is just the cube root of the expression itself. The original expression can be written in radical form as √[3]{(16x^{-2/3})y}
To simplify this further, we take the cube root of each part individually. The cube root of a product is equal to the product of the cube roots. Therefore, we can express the simplified version as √[3]{16} × √[3]{x^{-2/3}} × √[3]{y}. As 16 is a perfect cube (2^4), we know that √[3]{16} is 2. So, the final expression in radical form is 2x^{-2/9}√[3]{y}.