Final answer:
The expression (100x^2)^(-1/2) simplifies to 1/10x by applying the property that a negative exponent represents the reciprocal of a term, and taking the square root of 100 and x^2.
Step-by-step explanation:
The expression (100x2)(-1/2) can be simplified using the rules of exponents. First, we recognize that a negative exponent indicates that the term is in the denominator.
Therefore, x-1 = 1/x. Applying this rule to the given expression, we get that (100x2)(-1/2) is equivalent to 1/√(100x2). Since the square root of 100 is 10 and the square root of x2 is x, the expression further simplifies to 1/10x.