Скачать или смотреть Prime factorization in power form- Mathematics Form 1 - Topic 2 - Factorization ( Lesson 2 out of 2)

Prime Factorization in Power Form

Introduction:

In the previous lesson, we learned about prime factors and how to find the prime factorization of a number.
Now, we will explore how to express the prime factorization in power form.
What is Power Form?

Power form is a way to express a number as the product of its prime factors using exponents (powers).
Expressing Prime Factorization in Power Form:

Consider a number, for example, 36.
First, find the prime factorization of 36, which we know is 2 x 2 x 3 x 3.
To express this in power form, we write it as 2^2 x 3^2.
The exponent (2 in this case) shows how many times the prime factor is repeated.
Rules for Expressing in Power Form:

Find the prime factorization of the number.
Write down the prime factors as a product with exponents.
If a prime factor is repeated, use an exponent to indicate how many times it is repeated.
If a prime factor appears only once, its exponent is 1.
Example 1: Express 60 in Power Form:

Prime factorization of 60: 2 x 2 x 3 x 5.
In power form: 2^2 x 3 x 5.
Example 2: Express 90 in Power Form:

Prime factorization of 90: 2 x 3 x 3 x 5.
In power form: 2 x 3^2 x 5.
Example 3: Express 126 in Power Form:

Prime factorization of 126: 2 x 3 x 3 x 7.
In power form: 2 x 3^2 x 7.
Example 4: Express 49 in Power Form:

Prime factorization of 49: 7 x 7.
In power form: 7^2.
Benefits of Power Form:

Power form simplifies the representation of numbers with many factors.
It is a compact and convenient way to write factorizations.
It helps in performing operations with such numbers more efficiently.
Conclusion:

Power form is a useful way to express the prime factorization of a number using exponents.
It simplifies the representation of numbers and is handy in various mathematical calculations.
These notes should help you understand the concept of prime factorization in power form, a crucial topic in mathematics.