Question

evaluate $7^{-2}$. \
\
\bigcirc a. $-49$ \
\
\bigcirc b. $-14$ \
\
\bigcirc c. $\frac{1}{49}$ \
\
\bigcirc d. $-\frac{1}{49}$

Explanation:

Step1: Recall the negative exponent rule

The negative exponent rule states that \( a^{-n}=\frac{1}{a^{n}} \) for any non - zero real number \( a \) and positive integer \( n \). For \( 7^{-2} \), here \( a = 7 \) and \( n=2 \).

Step2: Apply the rule and calculate \( 7^{2} \)

First, apply the negative exponent rule: \( 7^{-2}=\frac{1}{7^{2}} \). Then, calculate \( 7^{2}=7\times7 = 49 \). So, \( 7^{-2}=\frac{1}{49} \).

Answer:

C. \(\frac{1}{49}\)