Let's work on solving the prime factorizations at the bottom of the page:

49. $2^2 \cdot 3^2 \cdot 5$

• $2^2 = 4$
• $3^2 = 9$
• $4 \cdot 9 = 36$
• $36 \cdot 5 = 180$

The number represented is 180.

50. $3^2 \cdot 5^2 \cdot 7$

• $3^2 = 9$
• $5^2 = 25$
• $9 \cdot 25 = 225$
• $225 \cdot 7 = 1575$

The number represented is 1575.

51. $2^3 \cdot 11^2 \cdot 13$

• $2^3 = 8$
• $11^2 = 121$
• $8 \cdot 121 = 968$
• $968 \cdot 13 = 12584$

The number represented is 12584.

Would you like any more details or clarifications on these calculations?

Here are five related questions to deepen understanding:

1. What is the prime factorization of 500?
2. How do you find the prime factorization of a number?
3. What is the greatest common divisor (GCD) of 180 and 1575?
4. Can two different numbers have the same prime factorization?
5. How can prime factorization help in simplifying fractions?

Tip: Prime factorizations are useful for finding the greatest common divisor (GCD) and least common multiple (LCM) between numbers.