1/∛x = x^(-1/3)
(x^(-1/3))^-6 = x^((-1/3)(-6)) = x^2
1/cubed root of x to -6 exponent
(x^(-1/3))^-6 = x^((-1/3)(-6)) = x^2
Step 1: Start with the expression 1/(∛x)^-6.
Step 2: Using the property of rational exponents that says (a/b)^c = a^c / b^c, we can rewrite the expression as 1/ (∛x)^-6 = 1/ [1/(∛x)^6].
Step 3: Next, we can simplify the expression within the brackets by applying the property of rational exponents that states (∛a)^b = a^(b/3). So, (∛x)^6 becomes x^(6/3) = x^2.
Step 4: Now, we can substitute x^2 back into 1/[1/(∛x)^6] to get 1/[1/x^2].
Step 5: Applying the property of rational exponents (1/a)^b = a^-b, we can rewrite the expression as [x^2]^(-1) = x^-2.
Therefore, the simplified expression in rational exponent form is x^-2.
In summary, we simplified the given expression 1/(∛x)^-6 to x^-2 by utilizing the properties of rational exponents.