When dividing exponents, what is the result of 1/x^m?

• A. x^m
• B. x^-m
• C. x^m/x^n
• D. 1/x^n

Answer: (B)

When dividing exponents, specifically in the case of (1/x^m), one can use the property of exponents that states (x^{-a} = 1/x^a).

In this case, (1/x^m) can be rewritten as (x^{-m}) because the negative exponent indicates that the base should be taken as 1 divided by the base raised to the positive exponent. Thus, expressing (1/x^m) with a negative exponent results in (x^{-m}).

This transformation follows the general rule of exponents that allows us to simplify expressions involving division of powers. Therefore, the representation of (1/x^m) as (x^{-m}) is consistent with exponent rules and validates the conclusion reached in the correct answer.