Without multiplying all the terms, verify these equalities. a) 10!= 6!7! b) 10!=7!5!3! c) 16!= 14!5!2! d) 9!=7!3!3!2!

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)

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step-by-step explanation: