Solve left(-6-3^5right)^-3left(-23^3-256right)^4/{left(9{3^2-256right)}^-2}

$$\frac{ { \left(-6- { 3 }^{ 5 } \right) }^{ -3 } { \left(-2 { 3 }^{ 3 } -256 \right) }^{ 4 } }{ { \left(9 { 3 }^{ 2 } -256 \right) }^{ -2 } }$$

Evaluate

$$-\frac{282828306250000}{15438249}\approx -18319973.090860239$$

Solution Steps

Calculate 3 to the power of 5 and get 243.

$$\frac{\left(-6-243\right)^{-3}\left(-2\times 3^{3}-256\right)^{4}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Subtract 243 from -6 to get -249.

$$\frac{\left(-249\right)^{-3}\left(-2\times 3^{3}-256\right)^{4}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Calculate -249 to the power of -3 and get -\frac{1}{15438249}.

$$\frac{-\frac{1}{15438249}\left(-2\times 3^{3}-256\right)^{4}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-\frac{1}{15438249}\left(-2\times 27-256\right)^{4}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Multiply -2 and 27 to get -54.

$$\frac{-\frac{1}{15438249}\left(-54-256\right)^{4}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Subtract 256 from -54 to get -310.

$$\frac{-\frac{1}{15438249}\left(-310\right)^{4}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Calculate -310 to the power of 4 and get 9235210000.

$$\frac{-\frac{1}{15438249}\times 9235210000}{\left(9\times 3^{2}-256\right)^{-2}}$$

Multiply -\frac{1}{15438249} and 9235210000 to get -\frac{9235210000}{15438249}.

$$\frac{-\frac{9235210000}{15438249}}{\left(9\times 3^{2}-256\right)^{-2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-\frac{9235210000}{15438249}}{\left(9\times 9-256\right)^{-2}}$$

Multiply 9 and 9 to get 81.

$$\frac{-\frac{9235210000}{15438249}}{\left(81-256\right)^{-2}}$$

Subtract 256 from 81 to get -175.

$$\frac{-\frac{9235210000}{15438249}}{\left(-175\right)^{-2}}$$

Calculate -175 to the power of -2 and get \frac{1}{30625}.

$$\frac{-\frac{9235210000}{15438249}}{\frac{1}{30625}}$$

Divide -\frac{9235210000}{15438249} by \frac{1}{30625} by multiplying -\frac{9235210000}{15438249} by the reciprocal of \frac{1}{30625}.

$$-\frac{9235210000}{15438249}\times 30625$$

Multiply -\frac{9235210000}{15438249} and 30625 to get -\frac{282828306250000}{15438249}.

$$-\frac{282828306250000}{15438249}$$

Factor

$$-\frac{282828306250000}{15438249} = -18319973\frac{1402723}{15438249} = -18319973.09086024$$