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

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

Evaluate

$$-\frac{1208925819436508291013025}{44115102527743250191613952}\approx -0.027403899$$

Solution Steps

Calculate 3 to the power of 5 and get 243.

$$\frac{\left(-6\times 243\right)^{-3}\left(-2\times 3\left(-256^{-2}\right)\right)^{4}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Multiply -6 and 243 to get -1458.

$$\frac{\left(-1458\right)^{-3}\left(-2\times 3\left(-256^{-2}\right)\right)^{4}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Calculate -1458 to the power of -3 and get -\frac{1}{3099363912}.

$$\frac{-\frac{1}{3099363912}\left(-2\times 3\left(-256^{-2}\right)\right)^{4}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Multiply -2 and 3 to get -6.

$$\frac{-\frac{1}{3099363912}\left(-6\left(-256^{-2}\right)\right)^{4}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Calculate 256 to the power of -2 and get \frac{1}{65536}.

$$\frac{-\frac{1}{3099363912}\left(-6\left(-\frac{1}{65536}\right)\right)^{4}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Multiply -6 and -\frac{1}{65536} to get \frac{3}{32768}.

$$\frac{-\frac{1}{3099363912}\times \left(\frac{3}{32768}\right)^{4}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Calculate \frac{3}{32768} to the power of 4 and get \frac{81}{1152921504606846976}.

$$\frac{-\frac{1}{3099363912}\times \frac{81}{1152921504606846976}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Multiply -\frac{1}{3099363912} and \frac{81}{1152921504606846976} to get -\frac{1}{44115102527743250191613952}.

$$\frac{-\frac{1}{44115102527743250191613952}}{\left(9\times 3^{2}-256^{5}\right)^{-2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-\frac{1}{44115102527743250191613952}}{\left(9\times 9-256^{5}\right)^{-2}}$$

Multiply 9 and 9 to get 81.

$$\frac{-\frac{1}{44115102527743250191613952}}{\left(81-256^{5}\right)^{-2}}$$

Calculate 256 to the power of 5 and get 1099511627776.

$$\frac{-\frac{1}{44115102527743250191613952}}{\left(81-1099511627776\right)^{-2}}$$

Subtract 1099511627776 from 81 to get -1099511627695.

$$\frac{-\frac{1}{44115102527743250191613952}}{\left(-1099511627695\right)^{-2}}$$

Calculate -1099511627695 to the power of -2 and get \frac{1}{1208925819436508291013025}.

$$\frac{-\frac{1}{44115102527743250191613952}}{\frac{1}{1208925819436508291013025}}$$

Divide -\frac{1}{44115102527743250191613952} by \frac{1}{1208925819436508291013025} by multiplying -\frac{1}{44115102527743250191613952} by the reciprocal of \frac{1}{1208925819436508291013025}.

$$-\frac{1}{44115102527743250191613952}\times 1208925819436508291013025$$

Multiply -\frac{1}{44115102527743250191613952} and 1208925819436508291013025 to get -\frac{1208925819436508291013025}{44115102527743250191613952}.

$$-\frac{1208925819436508291013025}{44115102527743250191613952}$$

Factor

$$-\frac{1208925819436508291013025}{44115102527743250191613952} = -0.027403899122216368$$