Properties of Powers with the Same Base

This page delves into the fundamental properties of exponents, particularly focusing on powers with the same base. The content is crucial for students studying potęga o wykładniku naturalnym klasa 7 pdf.

The first property introduced is the multiplication of powers with the same base:

Definition: am · an = am+n

This rule states that when multiplying powers with the same base, we add the exponents.

Several examples are provided to illustrate this concept:

Example: 2³ · 2⁴ · 2³⁺⁴ = 2⁷ = 128

This example demonstrates how to apply the rule when multiplying powers of 2.

Another example shows the application with powers of 10:

Example: 10³ · 10⁴ · 10⁻² = 10³⁺⁴⁻² = 10⁵ = 100000

The document then introduces the concept of raising a power to another power:

Definition: (am)n = am·n

This rule explains that when raising a power to another power, we multiply the exponents.

An example is provided to illustrate this concept:

Example: (5⁻³)⁻² = 5⁻³·⁻² = 5⁶

The page also covers the division of powers with the same base:

Definition: am ÷ an = am-n

This rule states that when dividing powers with the same base, we subtract the exponents.

An example is given to demonstrate this property:

Example: 2⁵ ÷ 2³ = 2⁵⁻³ = 2²

The document concludes with a complex example combining multiple properties:

Example: 4⁻¹² ÷ 4⁻¹⁵ · 4³ = 4⁻¹²⁺¹⁵⁺³ = 4⁶ = 4096

This comprehensive example showcases the application of multiple exponent rules in a single problem.

Highlight: Understanding these properties is crucial for działania na potęgach and forms the foundation for more advanced mathematical concepts.