˿

Index notation – WJECChallenging fractional indices

Indices are a way of representing numbers and letters that have been multiplied by themselves a number of times. They help us to complete problems involving powers more easily.

Part of MathsNumber

Challenging fractional indices

Combining negative and fractional indices

Example one

Evaluate \({81}^\frac{-1}{2}\)

Here, we have a combination of two different types of question – negative powers and fractional powers. If we deal with the negative in the power first, we can then work with the fraction.

\({81}^\frac{-1}{2} = \frac{1}{81^\frac{1}{2}}\)

= \(\frac{1}{\sqrt{81}}\)

= \(\frac{1}{9}\)

Example two

Evaluate \({16}^\frac{-3}{2}\)

\({16}^\frac{-3}{2} = \frac{1}{16^\frac{3}{2}}\)

= \(\frac{1}{(\sqrt{16})^{3}}\)

= \(\frac{1}{4^{3}}\)

= \(\frac{1}{64}\)

Question

Evaluate \({27}^\frac{-2}{3}\)

Next up
Test your understanding
Previous page
Fractional indices

More guides on this topic

Related links