Question

which expression is equivalent to $a^{-x}$?
a. $a^{1/x}$
b. $-a^x$
c. $\frac{1}{a^x}$
d. $-\frac{1}{a^x}$

Explanation:

Step1: Recall Negative Exponent Rule

The negative exponent rule states that for any non - zero number \(a\) and real number \(n\), \(a^{-n}=\frac{1}{a^{n}}\).

Step2: Apply the Rule to \(a^{-x}\)

In the expression \(a^{-x}\), we can think of \(n = x\). Using the negative exponent rule \(a^{-n}=\frac{1}{a^{n}}\), when \(n=x\), we get \(a^{-x}=\frac{1}{a^{x}}\).

Answer:

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