Question

7^{-2} simplifies to: options: does not simplify, 7^{1}, \frac{1}{7^{2}}, 7^{3}

Explanation:

Step1: Recall negative exponent rule

The rule for a negative exponent is \( a^{-n}=\frac{1}{a^{n}} \) where \( a
eq0 \) and \( n \) is a positive integer.

Step2: Apply the rule to \( 7^{-2} \)

Using the rule \( a^{-n}=\frac{1}{a^{n}} \) with \( a = 7 \) and \( n=2 \), we get \( 7^{-2}=\frac{1}{7^{2}} \).

Answer:

\(\frac{1}{7^{2}}\) (corresponding to the option with \(\frac{1}{7^{2}}\))