Final answer:
The simplified root form of 12^(5/8) × 12^(-1/2) is 12^(1/8), which represents the eighth root of 12.
Step-by-step explanation:
The question requires us to simplify the expression 12^(5/8) × 12^(-1/2) by finding the appropriate index for the root form.
To do this, we utilize the properties of exponents.
According to the rules of exponents, when we multiply expressions with the same base, we add the exponents:
(a^m × a^n = a^m+n).
In this case, a is 12, m is 5/8, and n is -1/2.
So the expression becomes 12^(5/8 - 1/2).
To simplify the exponents, we convert -1/2 to -4/8 to have a common denominator, turning the expression into 12^(5/8 - 4/8) = 12^(1/8), which represents the eighth root of 12.
Thus, 12^(1/8) is the root form of the original expression.