Final answer:
To find the cube root of x to the 15th power, you simply divide the exponent by the index of the root, resulting in x to the power of 5.
Step-by-step explanation:
To find the indicated root of ∛x¹⁵, we are looking for the cube root of x raised to the 15th power. Since exponents within a root can be divided by the index of the root (which is 3 in the case of a cube root), we can simplify the expression as follows:
x¹⁵³ = x⁵
This simplification is done by dividing the exponent by the index of the root: 15 / 3 = 5.
Therefore, x¹⁵ when subjected to the cube root is simply x⁵.