To simplify the expression (4x^2 y^-1/3)^3/14, you need to apply the exponent rules and simplify each part of the expression separately.
Let's start with (4x^2 y^-1/3). Raised to the power of 3/14, each term inside the parentheses will be raised to that exponent.
For the first term, 4x^2, raise the coefficient and the variable to the power of 3/14:
4^(3/14) * (x^2)^(3/14) = (2^2)^(3/14) * x^(2 * 3/14) = 2^(2 * 3/14) * x^(6/14) = 2^(6/14) * x^(3/7).
For the second term, y^-1/3, raise the variable to the power of 3/14:
(y^-1/3)^(3/14) = y^(-1/3 * 3/14) = y^(-1/14).
Now, put the simplified terms back together:
(4x^2 y^-1/3)^3/14 = 2^(6/14) * x^(3/7) * y^(-1/14).
So the simplified expression is 2^(6/14) * x^(3/7) * y^(-1/14).
Note: If you need a decimal approximation for the exponent, you can calculate using a calculator.