1. Let's start by understanding what power notation (also called exponents or indices) means. 2. Power notation is a way to express repeated multiplication of the same number. 3. For example, $a^n$ means multiplying $a$ by itself $n$ times: $$a^n = \underbrace{a \times a \times \cdots \times a}_{n \text{ times}}$$ 4. Here, $a$ is called the base, and $n$ is called the exponent or index. 5. Some important rules of indices are: - $a^m \times a^n = a^{m+n}$ (when multiplying powers with the same base, add the exponents) - $\frac{a^m}{a^n} = a^{m-n}$ (when dividing powers with the same base, subtract the exponents) - $(a^m)^n = a^{m \times n}$ (power of a power means multiply the exponents) - $a^0 = 1$ (any nonzero number raised to the zero power equals 1) - $a^{-n} = \frac{1}{a^n}$ (negative exponent means reciprocal) 6. Let's see an example: Simplify $2^3 \times 2^4$. Using the first rule: $$2^3 \times 2^4 = 2^{3+4} = 2^7 = 128$$ 7. Another example: Simplify $\frac{5^6}{5^2}$. Using the second rule: $$\frac{5^6}{5^2} = 5^{6-2} = 5^4 = 625$$ 8. Understanding these rules helps you work with powers and indices easily in algebra and other math topics. Final answer: Power notation $a^n$ means multiplying $a$ by itself $n$ times, and the rules above help simplify expressions with powers.