Solve -3/2-[3+4[2-(4/3-5/6)^{2}]]div(-3^{2}+(-4)^2-5^3*25^-1)^3

$$- \frac { 3 } { 2 } - [ 3 + 4 [ 2 - ( \frac { 4 } { 3 } - \frac { 5 } { 6 } ) ^ { 2 } ] ] \div ( - 3 ^ { 2 } + ( - 4 ) ^ { 2 } - 5 ^ { 3 } * 25 ^ { - 1 } ) ^ { 3 }$$

Evaluate

$$-\frac{11}{4}=-2.75$$

Solution Steps

Subtract \frac{5}{6} from \frac{4}{3} to get \frac{1}{2}.

$$-\frac{3}{2}-\frac{3+4\left(2-\left(\frac{1}{2}\right)^{2}\right)}{\left(-3^{2}+\left(-4\right)^{2}-5^{3}\times 25^{-1}\right)^{3}}$$

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

$$-\frac{3}{2}-\frac{3+4\left(2-\frac{1}{4}\right)}{\left(-3^{2}+\left(-4\right)^{2}-5^{3}\times 25^{-1}\right)^{3}}$$

Subtract \frac{1}{4} from 2 to get \frac{7}{4}.

$$-\frac{3}{2}-\frac{3+4\times \frac{7}{4}}{\left(-3^{2}+\left(-4\right)^{2}-5^{3}\times 25^{-1}\right)^{3}}$$

Multiply 4 and \frac{7}{4} to get 7.

$$-\frac{3}{2}-\frac{3+7}{\left(-3^{2}+\left(-4\right)^{2}-5^{3}\times 25^{-1}\right)^{3}}$$

Add 3 and 7 to get 10.

$$-\frac{3}{2}-\frac{10}{\left(-3^{2}+\left(-4\right)^{2}-5^{3}\times 25^{-1}\right)^{3}}$$

Calculate 3 to the power of 2 and get 9.

$$-\frac{3}{2}-\frac{10}{\left(-9+\left(-4\right)^{2}-5^{3}\times 25^{-1}\right)^{3}}$$

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

$$-\frac{3}{2}-\frac{10}{\left(-9+16-5^{3}\times 25^{-1}\right)^{3}}$$

Add -9 and 16 to get 7.

$$-\frac{3}{2}-\frac{10}{\left(7-5^{3}\times 25^{-1}\right)^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$-\frac{3}{2}-\frac{10}{\left(7-125\times 25^{-1}\right)^{3}}$$

Calculate 25 to the power of -1 and get \frac{1}{25}.

$$-\frac{3}{2}-\frac{10}{\left(7-125\times \frac{1}{25}\right)^{3}}$$

Multiply 125 and \frac{1}{25} to get 5.

$$-\frac{3}{2}-\frac{10}{\left(7-5\right)^{3}}$$

Subtract 5 from 7 to get 2.

$$-\frac{3}{2}-\frac{10}{2^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$-\frac{3}{2}-\frac{10}{8}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{2}-\frac{5}{4}$$

Subtract \frac{5}{4} from -\frac{3}{2} to get -\frac{11}{4}.

$$-\frac{11}{4}$$

Factor

$$-\frac{11}{4} = -2\frac{3}{4} = -2.75$$