Final answer:
The cube root of 27a¹²² is calculated by taking the cube root of 27 to get 3, and dividing the exponent of 'a' by 3 to yield 3a´°.
Step-by-step explanation:
The question asks to find the cube root of 27a¹²². To solve this, we first consider the cube root of the numeric part, which is 27, and then apply the rule for the cube root of an exponential expression. The cube root of 27 is 3, and according to the cubing of exponentials, we multiply the exponent of the variable by 1/3 when taking the cube root.
Thus, the cube root of 27a¹²² is 3a´°, since (122 * 1/3) equals 40. Hence, the correct answer is:
3a´°