Question

Resolva essa questão:
10 ÷ ³√-5⁰ - 1024²/4³^² + 3! + 0,0001 . 10⁵

$10 \div \sqrt[3]{ { - 5}^{0} } - \frac{ {1024}^{2} }{ { {4}^{3} }^{2} } + 3! + 0.0001 \times {10}^{5}$
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Answer 1

• Calculando essa expressão, temos:

   $\large\displaystyle\text{ \begin{gathered} \frac{10}{\sqrt[3]{-5^0}} -\frac{1024^2}{4^{3^2}} +3!+0,0001\cdot 10^5 = \boxed{\boxed{\green{2}}}\end{gathered} }$

Desejamos calcular a seguinte expressão:

$\large\displaystyle\text{ \begin{gathered} \frac{10}{\sqrt[3]{-5^0}} -\frac{1024^2}{4^{3^2}} +3!+0,0001\cdot 10^5 \end{gathered} }$

Primeiramente, temos que qualquer coisa elevada a zero é igual a um.

$\large\displaystyle\text{ \begin{gathered} \frac{10}{\sqrt[3]{-5^0}} -\frac{1024^2}{4^{3^2}} +3!+0,0001\cdot 10^5 \end{gathered} }$

$\large\displaystyle\text{ \begin{gathered} \frac{10}{\sqrt[3]{-1}} -\frac{1024^2}{4^{3^2}} +3!+0,0001\cdot 10^5 \end{gathered} }$

$\large\displaystyle\text{ \begin{gathered} -10 -\frac{1024^2}{4^{3^2}} +3!+0,0001\cdot 10^5 \end{gathered} }$

Iremos agora fatorar o 1024, transformando em uma fração de bases iguais. :)

$\large\displaystyle\text{ \begin{gathered} -10 -\frac{\left(4^5\right)^2}{4^{9}} +3!+0,0001\cdot 10^5 \end{gathered} }$

$\large\displaystyle\text{ \begin{gathered} -10 -\frac{4^{10}}{4^{9}} +6+\frac{1}{10000} \cdot 10^5 \end{gathered} }$

$\large\displaystyle\begin{gathered} -10 -4^{10-9} +6+\frac{1}{10000} \cdot 10^5 \end{gathered}$

$\large\displaystyle\begin{gathered} -10 -4+6+\frac{10\!\diagup\!\!\!\!0\!\diagup\!\!\!\!0\!\diagup\!\!\!\!0\!\diagup\!\!\!\!0}{1\!\diagup\!\!\!\!0\!\diagup\!\!\!\!0\!\diagup\!\!\!\!0\!\diagup\!\!\!\!0} \end{gathered}$

$\large\displaystyle\begin{gathered} -\!\diagup\!\!\!\!10 -4 +6+\!\diagup\!\!\!\!10\end{gathered}$

$\large\displaystyle\text{ \begin{gathered} \therefore \ \underline{\underline{2}}\ \checkmark\end{gathered} }$

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