Solve -2^2*(1-3/4)^2+sqrt{frac{32/128}}{(-1^2-1)^3-4.75-31/4}-sqrt{1.96}+sqrt[3]{64}*0.1=

$$\frac { - 2 ^ { 2 } \cdot ( 1 - \frac { 3 } { 4 } ) ^ { 2 } + \sqrt { \frac { 32 } { 128 } } } { ( - 1 ^ { 2 } - 1 ) ^ { 3 } - 4.75 - 3 \frac { 1 } { 4 } } - \sqrt { 1.96 } + \sqrt[ 3 ] { 64 } \cdot 0.1 =$$

Evaluate

$$-1.015625$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{-4\left(1-\frac{3}{4}\right)^{2}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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

$$\frac{-4\times \left(\frac{1}{4}\right)^{2}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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

$$\frac{-4\times \frac{1}{16}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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

$$\frac{-\frac{1}{4}+\sqrt{\frac{32}{128}}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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

$$\frac{-\frac{1}{4}+\sqrt{\frac{1}{4}}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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.

$$\frac{-\frac{1}{4}+\frac{1}{2}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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

$$\frac{\frac{1}{4}}{\left(-1^{2}-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Calculate 1 to the power of 2 and get 1.

$$\frac{\frac{1}{4}}{\left(-1-1\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Subtract 1 from -1 to get -2.

$$\frac{\frac{1}{4}}{\left(-2\right)^{3}-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

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

$$\frac{\frac{1}{4}}{-8-4.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Subtract 4.75 from -8 to get -12.75.

$$\frac{\frac{1}{4}}{-12.75-\frac{3\times 4+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Multiply 3 and 4 to get 12.

$$\frac{\frac{1}{4}}{-12.75-\frac{12+1}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Add 12 and 1 to get 13.

$$\frac{\frac{1}{4}}{-12.75-\frac{13}{4}}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Subtract \frac{13}{4} from -12.75 to get -16.

$$\frac{\frac{1}{4}}{-16}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Express \frac{\frac{1}{4}}{-16} as a single fraction.

$$\frac{1}{4\left(-16\right)}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Multiply 4 and -16 to get -64.

$$\frac{1}{-64}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Fraction \frac{1}{-64} can be rewritten as -\frac{1}{64} by extracting the negative sign.

$$-\frac{1}{64}-\sqrt{1.96}+\sqrt[3]{64}\times 0.1$$

Calculate the square root of 1.96 and get 1.4.

$$-\frac{1}{64}-1.4+\sqrt[3]{64}\times 0.1$$

Subtract 1.4 from -\frac{1}{64} to get -\frac{453}{320}.

$$-\frac{453}{320}+\sqrt[3]{64}\times 0.1$$

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

$$-\frac{453}{320}+4\times 0.1$$

Multiply 4 and 0.1 to get 0.4.

$$-\frac{453}{320}+0.4$$

Add -\frac{453}{320} and 0.4 to get -\frac{65}{64}.

$$-\frac{65}{64}$$

Factor

$$-1.015625$$