Question

1. $(3m)^{-2}$

Explanation:

Step1: Recall negative exponent rule

The negative exponent rule states that \(a^{-n}=\frac{1}{a^{n}}\) for any non - zero real number \(a\) and positive integer \(n\). Also, \((ab)^{n}=a^{n}b^{n}\) (power of a product rule). For \((3m)^{-2}\), we can apply the negative exponent rule first. So \((3m)^{-2}=\frac{1}{(3m)^{2}}\).

Step2: Apply power of a product rule

Using the power of a product rule \((ab)^{n}=a^{n}b^{n}\), where \(a = 3\), \(b=m\) and \(n = 2\), we have \((3m)^{2}=3^{2}\times m^{2}=9m^{2}\).

Step3: Substitute back

Substituting \((3m)^{2}=9m^{2}\) into \(\frac{1}{(3m)^{2}}\), we get \(\frac{1}{9m^{2}}\).

Answer:

\(\frac{1}{9m^{2}}\)