Question

Se M =2³ e N =2², determine (M² . N³)²: *


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Answer 1

$\huge{ \bold{\red{ {2}^{ \small{24}} } }}$

explicaçao:

Se M =2³ e N =2², determine

$(M² . N³)²$

substituindo os valores dados.

$(( {2}^{3} )^{2} \: . \: ( {2}^{2})^{3} )²$

$⇩$

$( {2}^{6} \: . \: {2}^{6} )^{2}$

$⇩$

$( {2}^{12} )^{2}$

$⇩$

$\huge{ \bold{\red{ {2}^{ \small{24}} } }}$

Answer 2

$\large{ \boxed{ \boxed{ \tt {2}^{24} }}}$

Solução

Temos que:

$\tt \begin{cases} \tt \: M = {2}^{3} \\ \tt \: N = {2}^{2} \end{cases}$

Devemos calcular $\tt( {M}^{2} \cdot {N}^{3} {)}^{2}$. Substituindo os valores:

$\tt \iff(( {2}^{3} {)}^{2} \cdot( {2}^{2} {)}^{3} {)}^{2} \\ \\ \tt \iff( {2}^{3 \cdot2} \cdot {2}^{2\cdot3} {)}^{2} \\ \\ \tt \iff( {2}^{6} \cdot {2}^{6} {)}^{2} \\ \\ \tt \iff( {2}^{6 + 6} {)}^{2} \\ \\ \tt \iff( {2}^{12} {)}^{2} \\ \\ \tt \iff {2}^{12\cdot2} \\ \\ \tt\therefore \: {2}^{24}$