Question

1. is the expression (3²)⁻³ equivalent to (3³)⁻²? explain. 23. model with math what is the width of the rectangle written as an exponential expression?

Explanation:

21.

Step1: Apply power - of - a - power rule

The power - of - a - power rule states that \((a^m)^n=a^{mn}\). For \((3^2)^{-3}\), we have \(a = 3\), \(m = 2\), and \(n=-3\), so \((3^2)^{-3}=3^{2\times(-3)}=3^{-6}\). For \((3^3)^{-2}\), we have \(a = 3\), \(m = 3\), and \(n=-2\), so \((3^3)^{-2}=3^{3\times(-2)}=3^{-6}\).

Answer:

Yes, the expression \((3^2)^{-3}\) is equivalent to \((3^3)^{-2}\) because both simplify to \(3^{-6}\).

22. (There is no content for question 22 in the image, so this part is skipped)

23. (There is no information about the rectangle's related data in the image, so this part cannot be answered)