Powers and Exponents

This page introduces fundamental concepts of powers and exponents in mathematics, focusing on potęga o wykładniku wymiernym zadania and related operations.

The document begins by defining a power as the repeated multiplication of a number by itself. It illustrates this with the notation a^n, where 'a' is the base and 'n' is the exponent.

Definition: A power is represented as a^n, where 'a' is multiplied by itself 'n' times.

The page then presents formulas for powers with rational exponents, which are crucial for understanding potęga o wykładniku wymiernym zadania PDF. These formulas include:

1. The nth root of a: ∜a = a^(1/n)
2. The kth power of the nth root of a: (∜a)^k = a^(k/n)

Highlight: These formulas are essential for solving problems involving potęga o wykładniku rzeczywistym.

The document also covers działania na potęgach, presenting key rules for operations on powers:

1. Multiplication of powers with the same base: a^m · a^n = a^(m+n)
2. Division of powers with the same base: a^m ÷ a^n = a^(m-n)
3. Power of a power: (a^m)^n = a^(m·n)
4. Power of a product: (a · b)^n = a^n · b^n

Example: The document provides a specific example: 5^1 = (√5)^2

These rules are fundamental for solving problems related to działania na potęgach klasa 8 and działania na potęgach klasa 7.

Vocabulary:

• Potęga: Power
• Wykładnik: Exponent
• Pierwiastek: Root

The page serves as a comprehensive reference for students studying potęgi wzory and pierwiastki wzory, providing a solid foundation for more advanced mathematical concepts.