In previous activities, we have worked with positive integers, and we are now going to learn to evaluate numbers using negative indices.

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 finding the "reciprocal" of

For example

Evaluate 2^{-3} means work out the value of

We have found the reciprocal of 2^{3}

Evaluate 3^{-4} means work out the value of

We have found the reciprocal of 3^{4}

We will work out some questions like this, and then try to evaluate negative indices with negative numbers and fractions