Resolver [(2/3)^{2}*(-2/3)^{3}*(-2/3)^{4}]^{2}:[-(-2/3)^{5}]^3+(-frac{2}{3})^3-(frac{2}{7})^4*(-frac{7}{4})^4

$$[ ( \frac { 2 } { 3 } ) ^ { 2 } \cdot ( - \frac { 2 } { 3 } ) ^ { 3 } \cdot ( - \frac { 2 } { 3 } ) ^ { 4 } ] ^ { 2 } : [ - ( - \frac { 2 } { 3 } ) ^ { 5 } ] ^ { 3 } + ( - \frac { 2 } { 3 } ) ^ { 3 } - ( \frac { 2 } { 7 } ) ^ { 4 } \cdot ( - \frac { 7 } { 4 } ) ^ { 4 }$$

Avaliar

$$-\frac{1}{16}=-0,0625$$

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some 3 e 4 para obter 7.

$$\frac{\left(\left(\frac{2}{3}\right)^{2}\left(-\frac{2}{3}\right)^{7}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule \frac{2}{3} elevado a 2 e obtenha \frac{4}{9}.

$$\frac{\left(\frac{4}{9}\left(-\frac{2}{3}\right)^{7}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule -\frac{2}{3} elevado a 7 e obtenha -\frac{128}{2187}.

$$\frac{\left(\frac{4}{9}\left(-\frac{128}{2187}\right)\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Multiplique \frac{4}{9} e -\frac{128}{2187} para obter -\frac{512}{19683}.

$$\frac{\left(-\frac{512}{19683}\right)^{2}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule -\frac{512}{19683} elevado a 2 e obtenha \frac{262144}{387420489}.

$$\frac{\frac{262144}{387420489}}{\left(-\left(-\frac{2}{3}\right)^{5}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule -\frac{2}{3} elevado a 5 e obtenha -\frac{32}{243}.

$$\frac{\frac{262144}{387420489}}{\left(-\left(-\frac{32}{243}\right)\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

O oposto de -\frac{32}{243} é \frac{32}{243}.

$$\frac{\frac{262144}{387420489}}{\left(\frac{32}{243}\right)^{3}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule \frac{32}{243} elevado a 3 e obtenha \frac{32768}{14348907}.

$$\frac{\frac{262144}{387420489}}{\frac{32768}{14348907}}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Divida \frac{262144}{387420489} por \frac{32768}{14348907} ao multiplicar \frac{262144}{387420489} pelo recíproco de \frac{32768}{14348907}.

$$\frac{262144}{387420489}\times \frac{14348907}{32768}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Multiplique \frac{262144}{387420489} e \frac{14348907}{32768} para obter \frac{8}{27}.

$$\frac{8}{27}+\left(-\frac{2}{3}\right)^{3}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule -\frac{2}{3} elevado a 3 e obtenha -\frac{8}{27}.

$$\frac{8}{27}-\frac{8}{27}-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Subtraia \frac{8}{27} de \frac{8}{27} para obter 0.

$$0-\left(\frac{2}{7}\right)^{4}\left(-\frac{7}{4}\right)^{4}$$

Calcule \frac{2}{7} elevado a 4 e obtenha \frac{16}{2401}.

$$0-\frac{16}{2401}\left(-\frac{7}{4}\right)^{4}$$

Calcule -\frac{7}{4} elevado a 4 e obtenha \frac{2401}{256}.

$$0-\frac{16}{2401}\times \frac{2401}{256}$$

Multiplique \frac{16}{2401} e \frac{2401}{256} para obter \frac{1}{16}.

$$0-\frac{1}{16}$$

Subtraia \frac{1}{16} de 0 para obter -\frac{1}{16}.

$$-\frac{1}{16}$$

Fatorizar

$$-\frac{1}{16} = -0,0625$$