Question

. O símbolo ! é usado para representar o produto dos números naturais de 1 a , isto é, ! = ⋅ ( − 1) … 2 ⋅ 1. Por exemplo, 4! = 4 ⋅ 3 ⋅ 2 ⋅ 1. Se ! = 2¹⁵ ⋅ 3⁶ ⋅ 5³ ⋅ 7²⋅ 11 ⋅ 13, qual é o valor de ?
A) 13
B) 14
C) 15
D) 16
E) 18​

Answer 1

Resposta:

D) 16

Explicação passo a passo:

X! = 2¹⁵ ⋅ 3⁶ ⋅ 5³ ⋅ 7²⋅ 11 ⋅ 13

X! = 32768 ⋅ 729 ⋅ 125 ⋅ 49 ⋅ 143

X! = 23 887 872 ⋅ 125 ⋅ 7007

X! = 23 887 872 ⋅ 875875

X! = 20 922 789 888 000

2 ⋅ 3 = 6

6 ⋅ 4 = 24

24 ⋅ 5 = 120

120 ⋅ 6 = 720

720 ⋅ 7 = 5 040

5 040 ⋅ 8 = 40 320

40 320 ⋅ 9 = 362 880

362 880 ⋅ 10 = 3 628 800

3 628 800 ⋅ 11 = 39 916 800

39 916 800 ⋅ 12 = 479 001 600

479 001 600 ⋅ 13 = 6 227 020 800

6 227 020 800 ⋅ 14 = 87 178 291 200

87 178 291 200 ⋅ 15 = 1 307 674 368 000

1 307 674 368 000 ⋅ 16 = 20 922 789 888 000

X! = 16!

X = 16