Indices & the Law of Indices

Question

Simplify \(\left(3a\right)^{-2}\)

Solution

Show solution Hide solution Fully worked — 3 steps

1. 1
   Apply the negative-index law \(a^{-m} = \frac{1}{a^{m}}\)

   \[ \left(3a\right)^{-2} = \frac{1}{\left(3a\right)^{2}} \]
2. 2
   Apply the power-of-a-product law \((ab)^{n} = a^{n}b^{n}\)

   \[ = \frac{1}{3^{2}a^{2}} \]
3. Evaluate \(3^{2}\)

   \[ \left(3a\right)^{-2} = \frac{1}{9a^{2}} \]

   That is, the simplified expression is 1 over 9 a squared.