Properties of Exponents

This page covers the fundamental properties of exponents, which are crucial for simplifying and manipulating expressions with powers.

Key properties:

1. Any number raised to the power of 1 equals itself
2. Any number raised to the power of 0 equals 1
3. Product of powers with the same base: a^n · a^m = a^(n+m)
4. Quotient of powers with the same base: a^n ÷ a^m = a^(n-m)
5. Power of a product: (a · b)^n = a^n · b^n
6. Power of a quotient: (a ÷ b)^n = a^n ÷ b^n
7. Power of a power: (a^n)^m = a^(n·m)

Example:

• 2² · 2³ = 2^(2+3) = 2⁵
• 2⁵ ÷ 2³ = 2^(5-3) = 2²
• (3² · 2²) = 3² · 2² = 6²

Highlight: These properties are essential for solving potencias y raíces ejercicios resueltos (solved exponent and root exercises) efficiently.

The page includes practice problems to reinforce understanding of these properties.

Introduction to Integers

This page introduces the concept of números enteros (integers) and their representation on a number line.

Integers are defined as the set of whole numbers including positive, negative, and zero: Z = {..., -3, -2, -1, 0, 1, 2, 3, ...}

Key concepts covered:

• Ordering integers on a number line
• Absolute value of integers
• Opposite (additive inverse) of integers

Definition: The absolute value of a number is its distance from zero on the number line, regardless of sign.

Example:

• |6| = 6
• |-6| = 6

Exercises are provided to practice associating real-world scenarios with positive and negative integers, as well as locating integers on a number line.

Highlight: Understanding absolute value and opposites is crucial for working with operaciones con números enteros (operations with integers).

Ordering and Comparing Integers

This page focuses on ordering integers and performing basic addition and subtraction operations.

Key concepts:

• Ordering integers from least to greatest
• Evaluating true/false statements about integer relationships
• Adding and subtracting integers

Example: Ordering integers from least to greatest: -24 < -13 < -7 < -1 < 0 < +1 < +5 < +8 < +10

Several practice exercises are provided for mental calculation of integer addition and subtraction.

Highlight: When adding integers with different signs, subtract their absolute values and keep the sign of the larger number.

Vocabulary:

• Suma (addition)
• Resta (subtraction)

These concepts are fundamental for more advanced operaciones con números enteros 1 ESO (operations with integers in 1st year of secondary education).