If you confident with positive integers, we are now going to learn to evaluate numbers using** negative indices**.

If you are not sure what these are, why not review these before you move forwards?

Think about the patterns you can see in the following table:

Start with 1000 |
1000 | 10 x 10 x 10 | 10^{3} |

Then divide by 10 | 100 | 10 x 10 | 10^{2} |

Divide by 10 again | 10 | 10 | 10^{1} |

Divide by 10 again | 1 | 1 | 10^{0} Remember that any term to the power of 0 is 1 |

Divide by 10 again | 10^{-1} |
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Divide by 10 again | 10^{-2} |
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Divide by 10 again | 10^{-3} |

We can see that the pattern in these powers of 10 shows us that:

Notice that we are, in fact, finding the 'reciprocal' of:

**e.g. Evaluate 2 ^{-3}.**

This means work out the value of:

We have found the reciprocal of 2^{3}.

**e.g. Evaluate 3 ^{-4}.**

This means work out the value of:

We have found the reciprocal of 3^{4}.

In this activity, we will evaluate and calculate negative indices with negative numbers and fractions as we have seen in the examples above.

You may want to have a pen and paper handy before you start, so that you can compare your working to our answers written by a maths teacher.