Question

1. what is ( x^{-1} )?

a. ( \frac{1}{x} )
b. ( -x )
c. ( \frac{x}{1} )
d. ( x )

Explanation:

To determine what \( x^{-1} \) is, we use the negative exponent rule. The rule states that for any non - zero number \( a \) and integer \( n \), \( a^{-n}=\frac{1}{a^{n}} \). In the case of \( x^{-1} \), here \( a = x \) and \( n = 1 \). So applying the rule, we get \( x^{-1}=\frac{1}{x^{1}}=\frac{1}{x} \).

Now let's analyze the other options:

• Option b: \( -x \) is the negative of \( x \), which has nothing to do with the negative exponent rule applied to \( x \).
• Option c: \( \frac{x}{1}=x \), which is not equivalent to \( x^{-1} \).
• Option d: \( x \) is not equal to \( x^{-1} \) (except when \( x = 1 \) or \( x=- 1 \), but in general, the algebraic form of \( x^{-1} \) is \( \frac{1}{x} \)).

Answer:

a. \( \frac{1}{x} \)