Final answer:
The simplified form of ^7√x • ^7√x • ^7√x is found by adding the exponents of the same base and radical, resulting in x^(3/7), which is option B.
Step-by-step explanation:
The simplified form of the expression ^7√x • ^7√x • ^7√x involves understanding the properties of exponents and radicals. When we multiply expressions with the same base and radical, we add the exponents. In this case, since the root is the same (seventh root), we can think of each ^7√x as having an implicit exponent of 1/7. Therefore, when we multiply these three expressions together, we're effectively adding their exponents:
(x^(1/7)) • (x^(1/7)) • (x^(1/7)) = x^((1/7)+(1/7)+(1/7)) = x^(3/7).
Hence, the correct simplified form of ^7√x • ^7√x • ^7√x is x^(3/7), which corresponds to option B.