Indices (powers) can also be zero or negative. These extend the rules of indices and allow expressions to be written more compactly.

A zero index means the value of the expression is 1, as long as the base is not zero.

For example:

$$
5^0 = 1
$$

$$
10^0 = 1
$$

A negative index means the reciprocal of the corresponding positive power.

For example:

$$
2^{-1} = \frac{1}{2}
$$

$$
3^{-2} = \frac{1}{3^2} = \frac{1}{9}
$$

In general:

$$
a^{-n} = \frac{1}{a^n}
$$

Zero and negative indices are often used when simplifying expressions and solving algebraic problems.

You should be able to:

• Interpret expressions with zero indices
• Convert negative indices into fractions
• Use index rules consistently and accurately

Understanding zero and negative indices is essential for working confidently with algebra and powers.