Solve -2^2*(1-3/4)^2+sqrt{frac{32/128}}{(-1^2-1)^3-475-31/4}-sqrt{196}+sqrt[3]{64}*01=

$$\frac { - 2 ^ { 2 } \cdot ( 1 - \frac { 3 } { 4 } ) ^ { 2 } + \sqrt { \frac { 32 } { 128 } } } { ( - 1 ^ { 2 } - 1 ) ^ { 3 } - 475 - 3 \frac { 1 } { 4 } } - \sqrt { 196 } + \sqrt[ 3 ] { 64 } \cdot 01 =$$

Evaluate

$$-\frac{27231}{1945}\approx -14.000514139$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{-4\left(1-\frac{3}{4}\right)^{2}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

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

$$\frac{-4\times \left(\frac{1}{4}\right)^{2}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{-4\times \frac{1}{16}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Multiply -4 and \frac{1}{16} to get -\frac{1}{4}.

$$\frac{-\frac{1}{4}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Reduce the fraction \frac{32}{128} to lowest terms by extracting and canceling out 32.

$$\frac{-\frac{1}{4}+\sqrt{\frac{1}{4}}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Rewrite the square root of the division \frac{1}{4} as the division of square roots \frac{\sqrt{1}}{\sqrt{4}}. Take the square root of both numerator and denominator.

$$\frac{-\frac{1}{4}+\frac{1}{2}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

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

$$\frac{\frac{1}{4}}{\left(-1^{2}-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\frac{1}{4}}{\left(-1-1\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Subtract 1 from -1 to get -2.

$$\frac{\frac{1}{4}}{\left(-2\right)^{3}-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{1}{4}}{-8-475-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Subtract 475 from -8 to get -483.

$$\frac{\frac{1}{4}}{-483-\frac{3\times 4+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{1}{4}}{-483-\frac{12+1}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Add 12 and 1 to get 13.

$$\frac{\frac{1}{4}}{-483-\frac{13}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Subtract \frac{13}{4} from -483 to get -\frac{1945}{4}.

$$\frac{\frac{1}{4}}{-\frac{1945}{4}}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Divide \frac{1}{4} by -\frac{1945}{4} by multiplying \frac{1}{4} by the reciprocal of -\frac{1945}{4}.

$$\frac{1}{4}\left(-\frac{4}{1945}\right)-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Multiply \frac{1}{4} and -\frac{4}{1945} to get -\frac{1}{1945}.

$$-\frac{1}{1945}-\sqrt{196}+\sqrt[3]{64}\times 0\times 1$$

Calculate the square root of 196 and get 14.

$$-\frac{1}{1945}-14+\sqrt[3]{64}\times 0\times 1$$

Subtract 14 from -\frac{1}{1945} to get -\frac{27231}{1945}.

$$-\frac{27231}{1945}+\sqrt[3]{64}\times 0\times 1$$

Calculate \sqrt[3]{64} and get 4.

$$-\frac{27231}{1945}+4\times 0\times 1$$

Multiply 4 and 0 to get 0.

$$-\frac{27231}{1945}+0\times 1$$

Multiply 0 and 1 to get 0.

$$-\frac{27231}{1945}+0$$

Add -\frac{27231}{1945} and 0 to get -\frac{27231}{1945}.

$$-\frac{27231}{1945}$$

Factor

$$-\frac{27231}{1945} = -14\frac{1}{1945} = -14.000514138817481$$