Set Notation: A x B Product of Powers of Prime Factors

In summary, Set Notation: A x B Product of Powers of Prime Factors is a mathematical notation used to represent the product of two sets, where one set is composed of powers of prime factors. It is commonly used in number theory and algebraic equations and offers benefits such as concise representation and easier identification of prime factors. However, common mistakes include forgetting to include all prime factors and using incorrect notation symbols. Additionally, Set Notation can be applied to real-life scenarios in fields such as economics, engineering, and computer science to optimize resources and find efficient solutions.
  • #1
Natasha1
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Homework Statement
A = 2 x 3^43
B = 16 x 3^37
Relevant Equations
Express the numbers A x B as a product of powers of its prime factors. Give your answer in its simplest form.
I get 2^5 x 3^80

Am I correct?
 
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  • #2
Natasha1 said:
Homework Statement:: A = 2 x 3^43
B = 16 x 3^37
Relevant Equations:: Express the numbers A x B as a product of powers of its prime factors. Give your answer in its simplest form.

I get 2^5 x 3^80

Am I correct?
Yes
 
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Thank you
 

FAQ: Set Notation: A x B Product of Powers of Prime Factors

1. What is Set Notation?

Set notation is a mathematical language used to represent sets, which are collections of objects or numbers. It is a concise and efficient way to describe the elements of a set and their relationships.

2. What does "A x B Product of Powers of Prime Factors" mean in Set Notation?

In set notation, "A x B Product of Powers of Prime Factors" refers to the set of all possible combinations of numbers that can be formed by multiplying a number from set A with a number from set B, where both sets contain only prime numbers raised to different powers.

3. How is "A x B Product of Powers of Prime Factors" written in Set Notation?

The notation for "A x B Product of Powers of Prime Factors" is written as A x B = {ai * bj | ai ∈ A, bj ∈ B}, where ai and bj represent the elements of set A and B, respectively.

4. What is the purpose of using Set Notation for "A x B Product of Powers of Prime Factors"?

Using set notation for "A x B Product of Powers of Prime Factors" allows us to easily and efficiently represent all possible combinations of numbers that can be formed by multiplying elements from two sets of prime numbers. This notation is particularly useful in number theory and can help in solving problems related to prime factorization.

5. Are there any other variations of Set Notation for "A x B Product of Powers of Prime Factors"?

Yes, there are other variations of set notation for "A x B Product of Powers of Prime Factors" depending on the specific context or problem being addressed. Some examples include using subscript notation, using the "×" symbol instead of "x", or using set builder notation with specific conditions for the elements of set A and B.

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