Question

evaluate. write your answer as a fraction or whole number without exponents. $7^{-2} = \square$

Explanation:

Step1: Apply negative exponent rule

A negative exponent means taking the reciprocal of the base with a positive exponent: $a^{-n} = \frac{1}{a^n}$. For $7^{-2}$, this gives:
$\frac{1}{7^2}$

Step2: Calculate the positive exponent

Compute $7^2$:
$7^2 = 7 \times 7 = 49$

Step3: Write the final fraction

Substitute the result back into the reciprocal:
$\frac{1}{49}$

Answer:

$\frac{1}{49}$