Resolver (sqrt[3]{frac{1/216})^-1+3(2sqrt{9})^3-3sqrt{64}}{(-2)^0-(-1/2)+sqrt[4]{1/16}}

$$\frac { ( \sqrt[ 3 ] { \frac { 1 } { 216 } } ) ^ { - 1 } + 3 ( 2 \sqrt { 9 } ) ^ { 3 } - 3 \sqrt { 64 } } { ( - 2 ) ^ { 0 } - ( - \frac { 1 } { 2 } ) + \sqrt[ 4 ] { \frac { 1 } { 16 } } }$$

Avaliar

$$315$$

Passos Para a Resolução

Calcule \sqrt[3]{\frac{1}{216}} e obtenha \frac{1}{6}.

$$\frac{\left(\frac{1}{6}\right)^{-1}+3\times \left(2\sqrt{9}\right)^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calcule \frac{1}{6} elevado a -1 e obtenha 6.

$$\frac{6+3\times \left(2\sqrt{9}\right)^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calcule a raiz quadrada de 9 e obtenha 3.

$$\frac{6+3\times \left(2\times 3\right)^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Multiplique 2 e 3 para obter 6.

$$\frac{6+3\times 6^{3}-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calcule 6 elevado a 3 e obtenha 216.

$$\frac{6+3\times 216-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Multiplique 3 e 216 para obter 648.

$$\frac{6+648-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Some 6 e 648 para obter 654.

$$\frac{654-3\sqrt{64}}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calcule a raiz quadrada de 64 e obtenha 8.

$$\frac{654-3\times 8}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Multiplique -3 e 8 para obter -24.

$$\frac{654-24}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Subtraia 24 de 654 para obter 630.

$$\frac{630}{\left(-2\right)^{0}-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

Calcule -2 elevado a 0 e obtenha 1.

$$\frac{630}{1-\left(-\frac{1}{2}\right)+\sqrt[4]{\frac{1}{16}}}$$

O oposto de -\frac{1}{2} é \frac{1}{2}.

$$\frac{630}{1+\frac{1}{2}+\sqrt[4]{\frac{1}{16}}}$$

Some 1 e \frac{1}{2} para obter \frac{3}{2}.

$$\frac{630}{\frac{3}{2}+\sqrt[4]{\frac{1}{16}}}$$

Calcule \sqrt[4]{\frac{1}{16}} e obtenha \frac{1}{2}.

$$\frac{630}{\frac{3}{2}+\frac{1}{2}}$$

Some \frac{3}{2} e \frac{1}{2} para obter 2.

$$\frac{630}{2}$$

Dividir 630 por 2 para obter 315.

$$315$$

Fatorizar

$$3^{2}\times 5\times 7$$