Question

calcule:
a) 8!
b) 6!+4!
c)(3ao quadrado)!-(3!)ao quadrado
d) 10!/7!
e)100!/98!

por favor me ajudemm​

Answer 1

Explicação passo-a-passo:

a)

$\sf 8!=8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$

$\sf 8!=56\cdot30\cdot12\cdot2$

$\sf 8!=1680\cdot24$

$\sf \red{8!=40320}$

b)

• $\sf 6!=6\cdot5\cdot4\cdot3\cdot2\cdot1$

$\sf 6!=30\cdot12\cdot2$

$\sf 6!=360\cdot2$

$\sf 6!=720$

• $4!=4\cdot3\cdot2\cdot1$

$4!=12\cdot2$

$4!=24$

Assim:

$\sf 6!+4!=720+24$

$\sf \red{6!+4!=744}$

c)

• $\sf (3^2)!=9!$

$\sf (3^2)!=9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$

$\sf (3^2)!=72\cdot42\cdot20\cdot6$

$\sf (3^2)!=3024\cdot120$

$\sf (3^2)!=362880$

• $\sf (3!)^2=(3\cdot2\cdot1)^2$

$\sf (3!)^2=6^2$

$\sf (3!)^2=6\cdot6$

$\sf (3!)^2=36$

Logo:

$\sf (3^2)!-(3!)^2=362880-36$

$\sf \red{(3^2)!-(3!)^2=362844}$

d)

$\sf \dfrac{10!}{7!}=\dfrac{10\cdot9\cdot8\cdot7!}{7!}$

$\sf \dfrac{10!}{7!}=10\cdot9\cdot8$

$\sf \dfrac{10!}{7!}=90\cdot8$

$\sf \red{\dfrac{10!}{7!}=720}$

e)

$\sf \dfrac{100!}{98!}=\dfrac{100\cdot99\cdot98!}{98!}$

$\sf \dfrac{100!}{98!}=100\cdot99$

$\sf \red{\dfrac{100!}{98!}=9900}$