Question 1 How do you simplify 6 ! 5 ! ⋅ 8 ! 5!⋅8! 6! ? Answer 1 The factorial of any integer 𝑛 n is represented by 𝑛 ! = 𝑛 × ( 𝑛 − 1 ) × ( 𝑛 − 2 ) × ⋯ × 3 × 2 × 1 n!=n×(n−1)×(n−2)×⋯×3×2×1. To simplify 6 ! 5 ! ⋅ 8 ! 5!⋅8! 6! : Expand each factorial: 6 ! = 6 × 5 ! 6!=6×5! Substitute into the fraction: 6 ! 5 ! ⋅ 8 ! = 6 × 5 ! 5 ! ⋅ 8 ! 5!⋅8! 6! = 5!⋅8! 6×5! Cancel out 5 ! 5! in the numerator and denominator: = 6 8 ! = 1 280 = 8! 6 = 280 1 Result: 1 280 280 1 Question 2 Find the product of 30 30 and 610 610 . Express it in standard form. Give the value of 𝑎 a followed by the value of 𝑏 b separated by a comma. Answer 1 30 × 610 = 30 × 610 = 18300 30 × 610 = 30×610 = 18300 Simplify 18300 18300 by prime factorization: 18300 = 60 × 305 = 60 3 18300 = 60×305 =60 3 In the form 𝑎 ⋅ 𝑏 a⋅ b , we have 𝑎 = 60 a=60 and 𝑏 = 3 b=3. Result: 60, 3 Question 3 Find all factors of 54. Answer 1 The factors of 54 are: 1, 2, 3, 6, 9, 18, 27, and 54. Prime factorization: 54 = 2 × 3 × 3 × 3 = 2 × 3 3 54=2×3×3×3=2×3 3 Question 4 Find the square root of 256. Answer 1 The square root of 256 is: 256 = 16 256 =16 Question 5 How to list all the factors of 70? Answer 1 Write 70 as the product of its prime factors: 70 = 2 × 5 × 7 70=2×5×7 List the factor pairs: 1 × 70 1×70 2 × 35 2×35 5 × 14 5×14 7 × 10 7×10 All factors of 70 are: 1, 2, 5, 7, 10, 14, 35, 70.