Solve 3/4*[(-2+2/3):(-2)^-2-(1/4+2)*(3/2)^-3]^-2-(1-frac{1}{5})^-1-frac{37}{48}+1=

$$\frac { 3 } { 4 } \cdot [ ( - 2 + \frac { 2 } { 3 } ) : ( - 2 ) ^ { - 2 } - ( \frac { 1 } { 4 } + 2 ) \cdot ( \frac { 3 } { 2 } ) ^ { - 3 } ] ^ { - 2 } - ( 1 - \frac { 1 } { 5 } ) ^ { - 1 } - \frac { 37 } { 48 } + 1 =$$

Evaluate

$$-1$$

Solution Steps

Add -2 and \frac{2}{3} to get -\frac{4}{3}.

$$\frac{3}{4}\left(\frac{-\frac{4}{3}}{\left(-2\right)^{-2}}-\left(\frac{1}{4}+2\right)\times \left(\frac{3}{2}\right)^{-3}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Calculate -2 to the power of -2 and get \frac{1}{4}.

$$\frac{3}{4}\left(\frac{-\frac{4}{3}}{\frac{1}{4}}-\left(\frac{1}{4}+2\right)\times \left(\frac{3}{2}\right)^{-3}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Divide -\frac{4}{3} by \frac{1}{4} by multiplying -\frac{4}{3} by the reciprocal of \frac{1}{4}.

$$\frac{3}{4}\left(-\frac{4}{3}\times 4-\left(\frac{1}{4}+2\right)\times \left(\frac{3}{2}\right)^{-3}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Multiply -\frac{4}{3} and 4 to get -\frac{16}{3}.

$$\frac{3}{4}\left(-\frac{16}{3}-\left(\frac{1}{4}+2\right)\times \left(\frac{3}{2}\right)^{-3}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Add \frac{1}{4} and 2 to get \frac{9}{4}.

$$\frac{3}{4}\left(-\frac{16}{3}-\frac{9}{4}\times \left(\frac{3}{2}\right)^{-3}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Calculate \frac{3}{2} to the power of -3 and get \frac{8}{27}.

$$\frac{3}{4}\left(-\frac{16}{3}-\frac{9}{4}\times \frac{8}{27}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Multiply \frac{9}{4} and \frac{8}{27} to get \frac{2}{3}.

$$\frac{3}{4}\left(-\frac{16}{3}-\frac{2}{3}\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Subtract \frac{2}{3} from -\frac{16}{3} to get -6.

$$\frac{3}{4}\left(-6\right)^{-2}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Calculate -6 to the power of -2 and get \frac{1}{36}.

$$\frac{3}{4}\times \frac{1}{36}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

Multiply \frac{3}{4} and \frac{1}{36} to get \frac{1}{48}.

$$\frac{1}{48}-\left(1-\frac{1}{5}\right)^{-1}-\frac{37}{48}+1$$

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

$$\frac{1}{48}-\left(\frac{4}{5}\right)^{-1}-\frac{37}{48}+1$$

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

$$\frac{1}{48}-\frac{5}{4}-\frac{37}{48}+1$$

Subtract \frac{5}{4} from \frac{1}{48} to get -\frac{59}{48}.

$$-\frac{59}{48}-\frac{37}{48}+1$$

Subtract \frac{37}{48} from -\frac{59}{48} to get -2.

$$-2+1$$

Add -2 and 1 to get -1.

$$-1$$

Factor

$$-1$$