10 Questions
What is a whole number?
A positive integer, including 0, without fractions or decimals
What is the result of adding or multiplying two whole numbers?
Always a whole number
What does the commutative property of whole numbers state?
The order of whole numbers being added or multiplied does not change the result
What is the distributive property of whole numbers?
The multiplication of a whole number over the addition of two whole numbers
What does the exponent of a number indicate?
The power to which the base number should be raised
What is the result of a^0, except for 0^0?
1
What is the rule of exponents for a^m × a^n?
a^(m+n)
What is the purpose of using the rules of exponents in simplifying expressions?
To make the expressions more simple
What is the result of (a^m)^n?
a^(mn)
What is the definition of subtraction in whole numbers?
Finding the difference between two whole numbers
Study Notes
Whole Numbers
Definition
- A whole number is a positive integer, including 0, without fractions or decimals.
Properties
- Closure: The result of adding or multiplying two whole numbers is always a whole number.
- Commutative Property: The order of whole numbers being added or multiplied does not change the result.
- Associative Property: The order in which whole numbers are added or multiplied does not change the result.
- Distributive Property: The multiplication of a whole number over the addition of two whole numbers is equal to the sum of the multiplications.
Operations
- Addition: The result of combining two or more whole numbers.
- Subtraction: Finding the difference between two whole numbers.
- Multiplication: Repeated addition of a whole number.
- Division: Repeated subtraction of a whole number.
Exponents
Definition
- An exponent is a small number that indicates the power to which a base number should be raised.
Rules of Exponents
- Product of Powers: a^m × a^n = a^(m+n)
- Power of a Product: (ab)^m = a^m × b^m
- Power of a Power: (a^m)^n = a^(mn)
- Zero Exponent: a^0 = 1 (except for 0^0, which is undefined)
- Negative Exponent: a^(-m) = 1/a^m
Applications
- Simplifying Expressions: Using the rules of exponents to simplify expressions with exponents.
- Solving Equations: Using exponents to solve equations involving exponential functions.
Note: These notes provide a concise overview of whole numbers and exponents. For a more comprehensive understanding, it is recommended to practice problems and explore additional resources.
Whole Numbers
- A whole number is a positive integer, including 0, without fractions or decimals.
- Closure property: The result of adding or multiplying two whole numbers is always a whole number.
- Commutative property: The order of whole numbers being added or multiplied does not change the result.
- Associative property: The order in which whole numbers are added or multiplied does not change the result.
- Distributive property: Multiplication of a whole number over the addition of two whole numbers is equal to the sum of the multiplications.
Operations on Whole Numbers
- Addition: Combining two or more whole numbers.
- Subtraction: Finding the difference between two whole numbers.
- Multiplication: Repeated addition of a whole number.
- Division: Repeated subtraction of a whole number.
Exponents
- An exponent is a small number that indicates the power to which a base number should be raised.
- Product of powers: a^m × a^n = a^(m+n).
- Power of a product: (ab)^m = a^m × b^m.
- Power of a power: (a^m)^n = a^(mn).
- Zero exponent: a^0 = 1 (except for 0^0, which is undefined).
- Negative exponent: a^(-m) = 1/a^m.
Applications of Exponents
- Simplifying expressions: Using the rules of exponents to simplify expressions with exponents.
- Solving equations: Using exponents to solve equations involving exponential functions.
Learn about the definition and properties of whole numbers, including closure, commutative, associative, and distributive properties.
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