Solve frac{-(3^{2}*2)^{-4}*3^{4}}{(2*3)^{3}*2^2*3^3-(2^3-3)^-4}

$$\frac { - ( 3 ^ { 2 } \cdot 2 ) ^ { - 4 } \cdot 3 ^ { 4 } } { ( 2 \cdot 3 ) ^ { 3 } \cdot 2 ^ { 2 } \cdot 3 ^ { 3 } - ( 2 ^ { 3 } - 3 ) ^ { - 4 } }$$

Evaluate

$$-\frac{625}{18895678704}\approx -0.000000033$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

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

Multiply 9 and 2 to get 18.

$$\frac{\left(-18^{-4}\right)\times 3^{4}}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calculate 18 to the power of -4 and get \frac{1}{104976}.

$$\frac{-\frac{1}{104976}\times 3^{4}}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{-\frac{1}{104976}\times 81}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Multiply -\frac{1}{104976} and 81 to get -\frac{1}{1296}.

$$\frac{-\frac{1}{1296}}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Multiply 2 and 3 to get 6.

$$\frac{-\frac{1}{1296}}{6^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{-\frac{1}{1296}}{216\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{-\frac{1}{1296}}{216\times 4\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Multiply 216 and 4 to get 864.

$$\frac{-\frac{1}{1296}}{864\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{-\frac{1}{1296}}{864\times 27-\left(2^{3}-3\right)^{-4}}$$

Multiply 864 and 27 to get 23328.

$$\frac{-\frac{1}{1296}}{23328-\left(2^{3}-3\right)^{-4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-\frac{1}{1296}}{23328-\left(8-3\right)^{-4}}$$

Subtract 3 from 8 to get 5.

$$\frac{-\frac{1}{1296}}{23328-5^{-4}}$$

Calculate 5 to the power of -4 and get \frac{1}{625}.

$$\frac{-\frac{1}{1296}}{23328-\frac{1}{625}}$$

Subtract \frac{1}{625} from 23328 to get \frac{14579999}{625}.

$$\frac{-\frac{1}{1296}}{\frac{14579999}{625}}$$

Divide -\frac{1}{1296} by \frac{14579999}{625} by multiplying -\frac{1}{1296} by the reciprocal of \frac{14579999}{625}.

$$-\frac{1}{1296}\times \frac{625}{14579999}$$

Multiply -\frac{1}{1296} and \frac{625}{14579999} to get -\frac{625}{18895678704}.

$$-\frac{625}{18895678704}$$

Factor

$$-\frac{625}{18895678704} = -3.307634564445122 \times 10^{-8}$$