Resolver (31/8)^12*(8/7)^11*(-2)^3

$$( 3 \frac { 1 } { 8 } ) ^ { 12 } \times ( \frac { 8 } { 7 } ) ^ { 11 } \times ( - 2 ) ^ { 3 }$$

Avaliar

$$-\frac{59604644775390625}{1977326743}\approx -30144054,333154096$$

Passos Para a Resolução

Multiplique 3 e 8 para obter 24.

$$\left(\frac{24+1}{8}\right)^{12}\times \left(\frac{8}{7}\right)^{11}\left(-2\right)^{3}$$

Some 24 e 1 para obter 25.

$$\left(\frac{25}{8}\right)^{12}\times \left(\frac{8}{7}\right)^{11}\left(-2\right)^{3}$$

Calcule \frac{25}{8} elevado a 12 e obtenha \frac{59604644775390625}{68719476736}.

$$\frac{59604644775390625}{68719476736}\times \left(\frac{8}{7}\right)^{11}\left(-2\right)^{3}$$

Calcule \frac{8}{7} elevado a 11 e obtenha \frac{8589934592}{1977326743}.

$$\frac{59604644775390625}{68719476736}\times \frac{8589934592}{1977326743}\left(-2\right)^{3}$$

Multiplique \frac{59604644775390625}{68719476736} e \frac{8589934592}{1977326743} para obter \frac{59604644775390625}{15818613944}.

$$\frac{59604644775390625}{15818613944}\left(-2\right)^{3}$$

Calcule -2 elevado a 3 e obtenha -8.

$$\frac{59604644775390625}{15818613944}\left(-8\right)$$

Multiplique \frac{59604644775390625}{15818613944} e -8 para obter -\frac{59604644775390625}{1977326743}.

$$-\frac{59604644775390625}{1977326743}$$

Fatorizar

$$-\frac{59604644775390625}{1977326743} = -30144054\frac{658754502}{1977326743} = -30144054,333154093$$