1. Let's start by understanding what indices (or exponents) are. An index tells us how many times to multiply a number by itself. For example, $a^n$ means multiply $a$ by itself $n$ times. 2. The basic rules of indices are: - Product rule: $a^m \times a^n = a^{m+n}$ - Quotient rule: $\frac{a^m}{a^n} = a^{m-n}$ - Power rule: $(a^m)^n = a^{m \times n}$ - Zero exponent: $a^0 = 1$ (for $a \neq 0$) - Negative exponent: $a^{-n} = \frac{1}{a^n}$ 3. Let's do an example: Simplify $2^3 \times 2^4$. Using the product rule, add the exponents: $2^{3+4} = 2^7$. 4. Another example: Simplify $\frac{5^6}{5^2}$. Using the quotient rule, subtract the exponents: $5^{6-2} = 5^4$. 5. For a power of a power: Simplify $(3^2)^4$. Multiply the exponents: $3^{2 \times 4} = 3^8$. 6. Remember, if you have a negative exponent like $4^{-3}$, rewrite it as $\frac{1}{4^3}$. 7. Practice these rules step-by-step to master indices!