Understanding Powers and Scientific Notation
The first page introduces fundamental concepts of powers and their properties, along with scientific notation.
Definition: A power consists of two parts - the base number and the exponent, where the base is multiplied by itself the number of times indicated by the exponent.
Example: 2² = 2 × 2 = 4 and 5⁴ = 5 × 5 × 5 × 5 = 625
The page covers several key properties of własności potęg:
Highlight: For any non-zero number a and natural number n:
- If a > 0, then aⁿ > 0
- If a < 0 and n is even, then aⁿ > 0
- If a < 0 and n is odd, then aⁿ < 0
Definition: Notacja wykładnicza represents positive numbers as a product a × 10ⁿ, where n is an integer and 1 ≤ a < 10.
Example: 500 = 5 × 10² and 0.05 = 5 × 10⁻²
The page concludes with działania na potęgach (operations with powers):
Vocabulary: Key operations include:
- Multiplication: aⁿ × aᵐ = aⁿ⁺ᵐ
- Division: aⁿ ÷ aᵐ = aⁿ⁻ᵐ
- Power of a power: (aⁿ)ᵐ = aⁿᵐ
Highlight: For negative exponents, the power can be written as a fraction: a⁻ⁿ = 1/aⁿ