Final answer:
The cube root of -27x^12 is -3x^4, found by separately taking the cube root of -27 as -3 and dividing the exponent 12 by 3 for the variable x, giving x^4.
Step-by-step explanation:
The cube root of -27x12 can be calculated by finding the cube root of each factor separately. Recall that the cube root of a product is the product of the cube roots. Here, -27 is the cube of -3, while x12 is a perfect cube because 12 is divisible by 3. By the properties of exponents, we know that to find the cube root of an exponential term, you can divide the exponent by 3.
Therefore, the cube root of -27x12 is equal to the cube root of -27 multiplied by the cube root of x12, which is:
∛(-27x12) = ∛(-27) × ∛(x12)
= (-3) × x4
The final answer is -3x4.