Answer:
a)10! = 6×5×4×3×2 ×7!
10! = 6! 7! (Verified)
b)10! = 3! × 5! × 7! = 7!5!3! (Verified)
c)16! = 2! × 5! × 14!
16! = 14!5!2! (Verified)
d)9! = 3! × 3! ×2! × 7!
9! = 7!3!3!2! (Verified)
Step-by-step explanation:
a) 10!= 6!7!
10! = 10×9×8×7!
Reducing to their lowest factors
10! = (2×5)×(3×3)×(2×2×2) × 7!
Rearranging the factors, we have;
10! = (2×3)×(5)×(2×2)×(3)×2 × 7!
10! = 6×5×4×3×2 ×7!
10! = 6! 7! (Verified)
b) 10!=7!5!3!
10! = 10×9×8×7!
10! = (2×5)×(3×3)×(2×2×2) × 7!
Rearranging the factors, we have;
10! = (2×3)×(5)×(2×2)×(3)×2× 7!
10! = (3×2×1) × (5×4×3×2×1) × 7!
10! = 3! × 5! × 7! = 7!5!3! (Verified)
c) 16!= 14!5!2!
16! = 16×15×14!
16! = (2×2×2×2) × (5×3) × 14!
Rearranging the factors.
16! = (2) × (5) × (2×2) × (3) × (2) ×14!
16! = (2!) ×(5×4×3×2) × 14!
16! = 2! × 5! × 14!
16! = 14!5!2! (Verified)
d) 9!=7!3!3!2
9! = 9×8×7!
9! = (3×3) × (2×2×2) × 7!
Rearranging the factors
9! = (3×2) ×(3×2) ×(2) × 7!
9! = 3! × 3! ×2! × 7!
9! = 7!3!3!2! (Verified)
