Exploring Prime Factorization with Exponents

The video tutorial covers the concept of exponents and their application in prime factorization. It begins with an example using the number 100, demonstrating how to express repeated factors with exponents. The tutorial then explores the prime factorization of 72 and 135, emphasizing the use of exponents for simplification. A problem-solving section on the prime factorization of 360 is included, with a focus on evaluating multiple-choice answers. The video also addresses common mistakes in prime factorization, using the number 24 as an example. Finally, a homework assignment is provided to reinforce the concepts learned.

What is the prime factorization of 100 using exponents?

• 2^3 * 5^2

• 2^3 * 5^3

• 2^2 * 5^2

• 2^2 * 5^3

Which of the following is the prime factorization of 72 using exponents?

• 2^3 * 3^2

• 2^2 * 3^3

• 2^3 * 3^3

• 2^2 * 3^2

What is the prime factorization of 72?

• 2^3 * 3^2

• 2^2 * 3^3

• 2^2 * 3^2

• 2^3 * 3^3

What is the prime factorization of 135 using exponents?

• 3^3 * 5

• 3^2 * 5^2

• 3^3 * 5^2

• 3^2 * 5

Which of the following is the correct prime factorization of 360?

• 2^3 * 3^3 * 5

• 2^2 * 3^2 * 5

• 2^3 * 3^2 * 5

• 2^2 * 3^3 * 5

What is the prime factorization of 360?

• 2^3 * 3^2 * 5

• 2^2 * 3^3 * 5

• 2^3 * 3^3 * 5

• 2^2 * 3^2 * 5

Is the prime factorization of 24 given by Jessica correct?

• No, because 24 cannot be factorized

• Yes, because 2 and 3 are prime numbers

• No, because 4 is not a prime number

• Yes, because 2 * 3 * 4 equals 24

Which number does not belong in the set: 24, 12, 2, 11?

• 12

• 24

• 11

• 2

Which is greater: 2^5 or 5^2?

• Cannot be determined

• They are equal

• 5^2

• 2^5

Does every number have a prime factorization?

• Yes, because every number can be broken down into prime factors

• No, because some numbers are already prime

• Yes, because prime factorization is a fundamental property of numbers

• No, because some numbers cannot be factorized