Answer:
To write the expression (16x^4 y^6)^(-2/3) as a radical expression in the simplest form, we can use the property that (a^m)^n = a^(m*n), where a is a non-negative number and m and n are any real numbers. Applying this property, we get:
(16x^4 y^6)^(-2/3) = [(16x^4 y^6)^(1/3)]^(-2)
Now, we need to simplify the expression inside the square brackets. We can factor 16 as 2^4, and since we're taking the cube root, we can take out one factor of 2 from each term inside the parentheses:
(16x^4 y^6)^(1/3) = [(2^4 x^4 y^6)^(1/3)] = 2x^(4/3) y^(2)
Substituting this into the previous expression, we get:
(16x^4 y^6)^(-2/3) = [2x^(4/3) y^(2)]^(-2) = 1/[2^2 x^(4/3 * 2) y^(2*2)] = 1/(4x^(8/3) y^(4))
Therefore, the expression (16x^4 y^6)^(-2/3) can be written as 1/(4x^(8/3) y^(4)) in the simplest radical form.