Page 2: Negative Exponents and Scientific Notation

This page focuses on working with negative exponents and expressing numbers in scientific notation using powers of 10. It provides comprehensive examples of converting between standard and scientific notation.

Definition: A negative exponent indicates the reciprocal of the positive exponent $a⁻ⁿ = 1/aⁿ$

Example: 2⁻³ = 1/2³ = 1/8

Highlight: Large numbers and very small decimals can be expressed using powers of 10:

• 1 Million = 10⁶
• 1 Billion = 10¹²
• 0.001 = 10⁻³

Vocabulary:

• Zehnerpotenz: Power of ten
• Produkt: Product
• Komma: Decimal point

The page concludes with various problem types and methods for converting numbers to and from scientific notation, emphasizing the importance of proper decimal placement and exponent selection.

Page 1: Basic Power Rules and Operations

This page introduces fundamental concepts of exponents and explains the Potenzregeln für gleiche Basis (power rules for the same base). The content covers multiplication, division, and power operations with exponential expressions.

Definition: A power consists of a base number and an exponent, where the base is multiplied by itself as many times as indicated by the exponent.

Example: 2³ means 2 × 2 × 2 = 8

Highlight: When multiplying powers with the same base, add the exponents (aᵐ × aⁿ = aᵐ⁺ⁿ)

Vocabulary:

• Basis (base): The number being multiplied
• Exponent: The number of times the base is multiplied by itself
• Potenz (power): The result of the exponential expression

The page also covers rules for dividing powers with the same base and raising a power to another power, with detailed examples demonstrating each concept.