Algebra Practice Test

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