Resolver (sqrt{1/9}-[(1/3)^2:(1/2)^2*15-(05+22/3)+05]^3+frac{2}{3})

$$( \sqrt { \frac { 1 } { 9 } } - [ ( \frac { 1 } { 3 } ) ^ { 2 } : ( \frac { 1 } { 2 } ) ^ { 2 } \times 15 - ( 05 + 2 \frac { 2 } { 3 } ) + 05 ] ^ { 3 } + \frac { 2 } { 3 } )$$

Avaliar

$$-63$$

Passos Para a Resolução

Reescreva a raiz quadrada da divisão \frac{1}{9} à medida que a divisão de raízes quadradas \frac{\sqrt{1}}{\sqrt{9}}. Calcule a raiz quadrada do numerador e do denominador.

$$\frac{1}{3}-\left(\frac{\left(\frac{1}{3}\right)^{2}}{\left(\frac{1}{2}\right)^{2}}\times 15-\left(0\times 5+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Calcule \frac{1}{3} elevado a 2 e obtenha \frac{1}{9}.

$$\frac{1}{3}-\left(\frac{\frac{1}{9}}{\left(\frac{1}{2}\right)^{2}}\times 15-\left(0\times 5+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Calcule \frac{1}{2} elevado a 2 e obtenha \frac{1}{4}.

$$\frac{1}{3}-\left(\frac{\frac{1}{9}}{\frac{1}{4}}\times 15-\left(0\times 5+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Divida \frac{1}{9} por \frac{1}{4} ao multiplicar \frac{1}{9} pelo recíproco de \frac{1}{4}.

$$\frac{1}{3}-\left(\frac{1}{9}\times 4\times 15-\left(0\times 5+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Multiplique \frac{1}{9} e 4 para obter \frac{4}{9}.

$$\frac{1}{3}-\left(\frac{4}{9}\times 15-\left(0\times 5+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Multiplique \frac{4}{9} e 15 para obter \frac{20}{3}.

$$\frac{1}{3}-\left(\frac{20}{3}-\left(0\times 5+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Multiplique 0 e 5 para obter 0.

$$\frac{1}{3}-\left(\frac{20}{3}-\left(0+\frac{2\times 3+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Multiplique 2 e 3 para obter 6.

$$\frac{1}{3}-\left(\frac{20}{3}-\left(0+\frac{6+2}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Some 6 e 2 para obter 8.

$$\frac{1}{3}-\left(\frac{20}{3}-\left(0+\frac{8}{3}\right)+0\times 5\right)^{3}+\frac{2}{3}$$

Some 0 e \frac{8}{3} para obter \frac{8}{3}.

$$\frac{1}{3}-\left(\frac{20}{3}-\frac{8}{3}+0\times 5\right)^{3}+\frac{2}{3}$$

Subtraia \frac{8}{3} de \frac{20}{3} para obter 4.

$$\frac{1}{3}-\left(4+0\times 5\right)^{3}+\frac{2}{3}$$

Multiplique 0 e 5 para obter 0.

$$\frac{1}{3}-\left(4+0\right)^{3}+\frac{2}{3}$$

Some 4 e 0 para obter 4.

$$\frac{1}{3}-4^{3}+\frac{2}{3}$$

Calcule 4 elevado a 3 e obtenha 64.

$$\frac{1}{3}-64+\frac{2}{3}$$

Subtraia 64 de \frac{1}{3} para obter -\frac{191}{3}.

$$-\frac{191}{3}+\frac{2}{3}$$

Some -\frac{191}{3} e \frac{2}{3} para obter -63.

$$-63$$

Fatorizar

$$-63$$