Simplify \( \left(\sqrt[3]{64}a^3\right)^{-1} \).

To simplify the expression (643a3)−1, we can first simplify the term under the cube root sign. The cube root of 64a^3 is equal to the cube root of 64 multiplied by the cube root of a^3. The cube root of 64 is 4 because 4 x 4 x 4 = 64, and the cube root of a^3 is a multiplied by the cube root of a. Therefore, the term simplifies to 4a(cuberoot(a)). So, now we have (3√(4a(cuberoot(a))))^-1. To simplify this further, we can use the rule that (a/b)^-1 = b/a. Applying this rule to the expression, we get: 1 / (3√(4a(cuberoot(a)))) = (3√(4a(cuberoot(a))))^(-1) = 1 / (4a(cuberoot(a))) Therefore, the simplified expression is 1 / (4a(cuberoot(a))) or equivalently (1/4)(cuberoot(a^-2)). So the correct answer is 1/4cuberoot(a^-2), which can also be written as 14a.