Question

A soma dos algarismos do resultado da expressão numérica 5^23×2^33 é igual a:

a)5

b)6

c)7

d)8

Answer 1

Resposta:

$\boxed{\mathtt{C}}$

Explicação passo-a-passo:

$\\ \displaystyle \mathsf{5^{23} \cdot 2^{33} =} \\\\ \mathsf{5^{23} \cdot \left ( 2^{23} \cdot 2^{10} \right ) =} \\\\ \mathsf{\left ( 5^{23} \cdot 2^{23} \right ) \cdot 2^{10} =} \\\\ \mathsf{\left ( 5 \cdot 2 \right )^{23} \cdot 1024 =} \\\\ \mathsf{10^{23} \cdot 1024 =} \\\\ \boxed{\mathsf{1024\underbrace{0000\hdots000}_{23 \ zeros}}}$

Logo,

$\\ \displaystyle \mathsf{1 + 0 + 2 + 4 + 0 + 0 + \hdots + 0 =} \\\\ \boxed{\boxed{\mathsf{7}}}$