Indices (also called powers) are used as a shorter way of writing repeated multiplication. A positive integral index means the power is a positive whole number.

For example:

$$
2^3 = 2 \times 2 \times 2
$$

The number 2 is the base and the number 3 is the index.
This means 2 is multiplied by itself 3 times.

More examples:

$$
5^2 = 5 \times 5
$$

$$
10^4 = 10 \times 10 \times 10 \times 10
$$

An index of 1 means the number stays the same:

$$
7^1 = 7
$$

Positive integral indices are used to write large numbers more efficiently and are closely linked to prime factor decomposition and standard form.

You should be able to:

• Interpret expressions written using indices
• Expand expressions involving positive integral indices
• Use index notation correctly in calculations

Understanding index notation is essential for algebra, powers, and higher-level number work.

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