Question

a student thinks 3^(-2) means “-3 squared.” explain their mistake and correct it.

Explanation:

Step1: Identify 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. So \(3^{-2}=\frac{1}{3^{2}}\).

Step2: Analyze the student's mistake

The student misinterpreted the negative exponent as a negative sign in front of the base. \(- 3\) squared is \((-3)^{2}=(-3)\times(-3) = 9\), while \(3^{-2}\) is not the same as \((-3)^{2}\).

Step3: Calculate the correct value

Since \(3^{2}=3\times3 = 9\), then \(3^{-2}=\frac{1}{9}\).

Answer:

The student mistook the negative exponent for a negative sign on the base. The correct value of \(3^{-2}\) is \(\frac{1}{9}\).