Question

Efetue o cálculo de potenciação a seguir: (3³)²+(2²)²

Answer 1

Resposta:

Explicação passo a passo:

(3^3)^2 + (2^2)^2=

3^6+2^4=

729 + 16=

745

Answer 2

• O valor da expressão dada: (3³)²+(2²)² é igual a 745.

Para resolver sua questão, vale ressaltar as seguintes propriedades:

$\Large\displaystyle\text{ \begin{gathered} a^n=\underbrace{a\cdot a\cdot a\cdot a\cdot \ldots\cdot a}_{\large\displaystyle\begin{gathered} n\ vezes\end{gathered}}\ \ \red{(I)}.\end{gathered} }$

$\Large\displaystyle\begin{gathered} (a^b)^c = a^{bc}\ \ \red{(II)}. \end{gathered}$

Sabendo disso, temos que:

$\Large\displaystyle\begin{gathered} (3^3)^2+(2^2)^2 = 3^{3\cdot2}+2^{2\cdot2}\end{gathered}$

$\Large\displaystyle\begin{gathered} (3^3)^2+(2^2)^2 = 3^{6}+2^{4}\end{gathered}$

$\Large\displaystyle\begin{gathered} (3^3)^2+(2^2)^2 = (3\cdot3\cdot3\cdot3\cdot3\cdot3)+(2\cdot2\cdot2\cdot2)\end{gathered}$

$\Large\displaystyle\begin{gathered} (3^3)^2+(2^2)^2 = 729+16\end{gathered}$

$\Large\displaystyle\text{ \begin{gathered}\therefore \green{\underline{\boxed{ (3^3)^2+(2^2)^2 =745}}}\ \ (\checkmark).\end{gathered} }$

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