Exploring Prime Factorization and Exponents

The video tutorial covers generating equivalent numerical expressions using order of operations, focusing on whole number exponents and prime factorization. It demonstrates how these concepts work together through problem-solving examples from a math textbook. The tutorial includes calculating the prime factorization of sums and areas, emphasizing the use of exponents to express these factorizations. The video concludes with a practical example involving the prime factorization of a smaller pool's area.

What mathematical concepts are being used to generate equivalent numerical expressions?

• Geometry and Algebra

• Multiplication and Division

• Order of Operations and Prime Factorization

• Addition and Subtraction

What page of the math textbook is referenced for the problems?

• Page 500

• Page 518

• Page 520

• Page 530

What is the smallest prime number used in the prime factorization of 216?

• 3

• 5

• 2

• 7

What is the exponent for the prime factor 2 in the prime factorization of 216?

• 3

• 2

• 5

• 4

What is the prime factorization of 216?

• 2^3 * 3^2

• 2^4 * 3^3

• 2^2 * 3^3

• 2^3 * 3^3

What is the area of the rectangle in the second example?

• 18,000

• 1,800

• 1,250

• 12,500

Which factor occurs exactly two times in the prime factorization of 18,000?

• 5

• 3

• 2

• 7

What is the prime factorization of 18,000?

• 2^4 * 3^2 * 5^3

• 2^2 * 3^4 * 5^3

• 2^3 * 3^2 * 5^4

• 2^4 * 3^3 * 5^2

What is the area of the smaller pool that is half the area of the Olympic-sized pool?

• 1,250

• 1,500

• 625

• 750

What is the prime factorization of 625?

• 5^3

• 5^5

• 5^4

• 5^2