1. The problem is to express a number or expression in index form, which means writing it as a power of a base. 2. The general formula for index form is $a^n$, where $a$ is the base and $n$ is the exponent or index. 3. Important rules: - $a^1 = a$ - $a^0 = 1$ (for $a \neq 0$) - $a^{-n} = \frac{1}{a^n}$ - $a^{m} \times a^{n} = a^{m+n}$ - $\left(a^m\right)^n = a^{mn}$ 4. To convert a number to index form, find the base and the exponent such that the number equals $a^n$. 5. Example: Express 16 in index form. - 16 can be written as $2^4$ because $2 \times 2 \times 2 \times 2 = 16$. 6. Therefore, 16 in index form is $2^4$. 7. This method applies to any number or expression that can be written as a power of a base.