Indices & the Law of Indices

Question

Simplify \(\left(\dfrac{5a}{b^{2}}\right)^{2}\)

Solution

Show solution Hide solution Fully worked — 2 steps

1. 1
   Apply the power-of-a-quotient law \(\left(\frac{a}{b}\right)^{n} = \frac{a^{n}}{b^{n}}\)

   \[ \left(\frac{5a}{b^{2}}\right)^{2} = \frac{5^{2}a^{2}}{b^{2 \times 2}} \]
2. Evaluate \(5^{2}\)

   The index \(2 \times 2\) evaluates to \(4\):

   \[ \left(\frac{5a}{b^{2}}\right)^{2} = \frac{25a^{2}}{b^{4}} \]

   That is, the simplified expression is 25 a squared, all over b to the power 4.