Algebra Practice Test 2025 – Complete Exam Preparation

To solve the equation \( 3^{-2} = \frac{1}{x} \), we first need to evaluate \( 3^{-2} \).

The negative exponent indicates that we are dealing with the reciprocal of \( 3^2 \). Thus, we can rewrite \( 3^{-2} \) as:

\[

3^{-2} = \frac{1}{3^2}

\]

Calculating \( 3^2 \) gives us \( 9 \). Therefore, \( 3^{-2} \) can be expressed as:

\[

3^{-2} = \frac{1}{9}

\]

Now we have the equation:

\[

\frac{1}{9} = \frac{1}{x}

\]

This indicates that \( x \) must equal \( 9 \) since both fractions are equal to each other in their reciprocal forms. To isolate \( x \), we can cross-multiply or simply recognize that for the two fractions to be equal, the denominators must be the same.

Thus, we deduce:

\[

x = 9

\]

This aligns with the calculation showing that when we apply the property of exponents correctly, the