Solve 297(2-4/5)^{2}:{[1/3+1-1/12-13/12(-frac{5}{9})^-7]*[frac{3^2}{6}-frac{(1-5)^2}{6}+frac{(-2)^2}{6}]}

$$297 ( 2 - \frac { 4 } { 5 } ) ^ { 2 } : \{ [ \frac { 1 } { 3 } + 1 - \frac { 1 } { 12 } - \frac { 13 } { 12 } ( - \frac { 5 } { 9 } ) ^ { - 7 } ] \cdot [ \frac { 3 ^ { 2 } } { 6 } - \frac { ( 1 - 5 ) ^ { 2 } } { 6 } + \frac { ( - 2 ) ^ { 2 } } { 6 } ] \}$$

Evaluate

$$-\frac{33412500}{2639603}\approx -12.658153518$$

Solution Steps

Subtract \frac{4}{5} from 2 to get \frac{6}{5}.

$$\frac{297\times \left(\frac{6}{5}\right)^{2}}{\left(\frac{1}{3}+1-\frac{1}{12}-\frac{13}{12}\left(-\frac{5}{9}\right)^{-7}\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Calculate \frac{6}{5} to the power of 2 and get \frac{36}{25}.

$$\frac{297\times \frac{36}{25}}{\left(\frac{1}{3}+1-\frac{1}{12}-\frac{13}{12}\left(-\frac{5}{9}\right)^{-7}\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Multiply 297 and \frac{36}{25} to get \frac{10692}{25}.

$$\frac{\frac{10692}{25}}{\left(\frac{1}{3}+1-\frac{1}{12}-\frac{13}{12}\left(-\frac{5}{9}\right)^{-7}\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Add \frac{1}{3} and 1 to get \frac{4}{3}.

$$\frac{\frac{10692}{25}}{\left(\frac{4}{3}-\frac{1}{12}-\frac{13}{12}\left(-\frac{5}{9}\right)^{-7}\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Subtract \frac{1}{12} from \frac{4}{3} to get \frac{5}{4}.

$$\frac{\frac{10692}{25}}{\left(\frac{5}{4}-\frac{13}{12}\left(-\frac{5}{9}\right)^{-7}\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Calculate -\frac{5}{9} to the power of -7 and get -\frac{4782969}{78125}.

$$\frac{\frac{10692}{25}}{\left(\frac{5}{4}-\frac{13}{12}\left(-\frac{4782969}{78125}\right)\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Multiply \frac{13}{12} and -\frac{4782969}{78125} to get -\frac{20726199}{312500}.

$$\frac{\frac{10692}{25}}{\left(\frac{5}{4}-\left(-\frac{20726199}{312500}\right)\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

The opposite of -\frac{20726199}{312500} is \frac{20726199}{312500}.

$$\frac{\frac{10692}{25}}{\left(\frac{5}{4}+\frac{20726199}{312500}\right)\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Add \frac{5}{4} and \frac{20726199}{312500} to get \frac{5279206}{78125}.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(\frac{3^{2}}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(\frac{9}{6}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(\frac{3}{2}-\frac{\left(1-5\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Subtract 5 from 1 to get -4.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(\frac{3}{2}-\frac{\left(-4\right)^{2}}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Calculate -4 to the power of 2 and get 16.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(\frac{3}{2}-\frac{16}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Reduce the fraction \frac{16}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(\frac{3}{2}-\frac{8}{3}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Subtract \frac{8}{3} from \frac{3}{2} to get -\frac{7}{6}.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(-\frac{7}{6}+\frac{\left(-2\right)^{2}}{6}\right)}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(-\frac{7}{6}+\frac{4}{6}\right)}$$

Reduce the fraction \frac{4}{6} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(-\frac{7}{6}+\frac{2}{3}\right)}$$

Add -\frac{7}{6} and \frac{2}{3} to get -\frac{1}{2}.

$$\frac{\frac{10692}{25}}{\frac{5279206}{78125}\left(-\frac{1}{2}\right)}$$

Multiply \frac{5279206}{78125} and -\frac{1}{2} to get -\frac{2639603}{78125}.

$$\frac{\frac{10692}{25}}{-\frac{2639603}{78125}}$$

Divide \frac{10692}{25} by -\frac{2639603}{78125} by multiplying \frac{10692}{25} by the reciprocal of -\frac{2639603}{78125}.

$$\frac{10692}{25}\left(-\frac{78125}{2639603}\right)$$

Multiply \frac{10692}{25} and -\frac{78125}{2639603} to get -\frac{33412500}{2639603}.

$$-\frac{33412500}{2639603}$$

Factor

$$-\frac{33412500}{2639603} = -12\frac{1737264}{2639603} = -12.658153517782788$$