Page 2: Advanced Exponent Rules and Special Cases

The second page delves into more advanced zasady potęgowania, including raising a power to another power and working with negative and fractional exponents. These concepts are crucial for students progressing to higher-level mathematics.

1. Raising a power to another power: When raising a power to another power, multiply the exponents. The rule is (a^m)^n = a^(m*n).

Example: (5^2)^4 = 5^8 illustrates the rule for raising a power to another power.

2. Negative exponents: A negative exponent indicates the reciprocal of the positive exponent. The rule is a^(-n) = (1/a)^n.

Highlight: Understanding negative exponents is crucial for working with fractions and reciprocals in algebraic expressions.

3. Fractional exponents: Fractional exponents represent roots. The rule is a^(m/n) = (n√a)^m, where n√ represents the nth root.

Vocabulary: The nth root of a number is a value that, when multiplied by itself n times, gives the number.

These advanced rules are essential for solving complex problems involving potęgi o wykładniku ujemnym and potęga o wykładniku wymiernym. They provide a foundation for understanding more sophisticated mathematical concepts and are particularly useful in algebra and calculus.

Page 1: Fundamental Rules of Exponents

The first page introduces the basic zasady potęgowania, focusing on operations with powers that have the same base or the same exponent. These rules are fundamental for understanding more complex operations with exponents.

Definition: In exponent notation, the base is the number being multiplied by itself, while the exponent indicates how many times the base is multiplied.

The page covers four main rules:

1. Multiplying powers with the same base: When multiplying powers with the same base, add the exponents. For example, a^m * a^n = a^(m+n).

2. Dividing powers with the same base: When dividing powers with the same base, subtract the exponents. For instance, a^m ÷ a^n = a^(m-n).

Highlight: Any number raised to the power of zero equals 1, which is a crucial concept in exponent operations.

3. Multiplying powers with the same exponent: When multiplying powers with the same exponent, multiply the bases and keep the exponent the same. For example, a^n * b^n = (a*b)^n.

4. Dividing powers with the same exponent: When dividing powers with the same exponent, divide the bases and keep the exponent the same. For instance, a^n ÷ b^n = (a÷b)^n.

Example: 5^2 * 5^4 = 5^6 demonstrates the rule for multiplying powers with the same base.

These rules form the foundation for działania na pierwiastkach and more advanced exponent operations.