Solve 33/4*2.6-3div(-11/3)/frac{1^{2-2^{3}+3^4+(-4)^5}{(-1)^2020*2}+0.28*99}*(-2)^2

$$\frac { 3 \frac { 3 } { 4 } \times 2.6 - 3 \div ( - 1 \frac { 1 } { 3 } ) } { \frac { 1 ^ { 2 } - 2 ^ { 3 } + 3 ^ { 4 } + ( - 4 ) ^ { 5 } } { ( - 1 ) ^ { 2020 } \times 2 } + 0.28 \times 99 } \times ( - 2 ) ^ { 2 }$$

Evaluate

$$-\frac{600}{5591}\approx -0.107315328$$

Solution Steps

Multiply 3 and 4 to get 12.

$$\frac{\frac{12+3}{4}\times 2.6-\frac{3}{-\frac{1\times 3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Add 12 and 3 to get 15.

$$\frac{\frac{15}{4}\times 2.6-\frac{3}{-\frac{1\times 3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Convert decimal number 2.6 to fraction \frac{26}{10}. Reduce the fraction \frac{26}{10} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{15}{4}\times \frac{13}{5}-\frac{3}{-\frac{1\times 3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Multiply \frac{15}{4} times \frac{13}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{15\times 13}{4\times 5}-\frac{3}{-\frac{1\times 3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Do the multiplications in the fraction \frac{15\times 13}{4\times 5}.

$$\frac{\frac{195}{20}-\frac{3}{-\frac{1\times 3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Reduce the fraction \frac{195}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{39}{4}-\frac{3}{-\frac{1\times 3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Multiply 1 and 3 to get 3.

$$\frac{\frac{39}{4}-\frac{3}{-\frac{3+1}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Add 3 and 1 to get 4.

$$\frac{\frac{39}{4}-\frac{3}{-\frac{4}{3}}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

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

$$\frac{\frac{39}{4}-3\left(-\frac{3}{4}\right)}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Express 3\left(-\frac{3}{4}\right) as a single fraction.

$$\frac{\frac{39}{4}-\frac{3\left(-3\right)}{4}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Multiply 3 and -3 to get -9.

$$\frac{\frac{39}{4}-\frac{-9}{4}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Fraction \frac{-9}{4} can be rewritten as -\frac{9}{4} by extracting the negative sign.

$$\frac{\frac{39}{4}-\left(-\frac{9}{4}\right)}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

The opposite of -\frac{9}{4} is \frac{9}{4}.

$$\frac{\frac{39}{4}+\frac{9}{4}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Since \frac{39}{4} and \frac{9}{4} have the same denominator, add them by adding their numerators.

$$\frac{\frac{39+9}{4}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Add 39 and 9 to get 48.

$$\frac{\frac{48}{4}}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Divide 48 by 4 to get 12.

$$\frac{12}{\frac{1^{2}-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Calculate 1 to the power of 2 and get 1.

$$\frac{12}{\frac{1-2^{3}+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{12}{\frac{1-8+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Subtract 8 from 1 to get -7.

$$\frac{12}{\frac{-7+3^{4}+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{12}{\frac{-7+81+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Add -7 and 81 to get 74.

$$\frac{12}{\frac{74+\left(-4\right)^{5}}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Calculate -4 to the power of 5 and get -1024.

$$\frac{12}{\frac{74-1024}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Subtract 1024 from 74 to get -950.

$$\frac{12}{\frac{-950}{\left(-1\right)^{2020}\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Calculate -1 to the power of 2020 and get 1.

$$\frac{12}{\frac{-950}{1\times 2}+0.28\times 99}\left(-2\right)^{2}$$

Multiply 1 and 2 to get 2.

$$\frac{12}{\frac{-950}{2}+0.28\times 99}\left(-2\right)^{2}$$

Divide -950 by 2 to get -475.

$$\frac{12}{-475+0.28\times 99}\left(-2\right)^{2}$$

Multiply 0.28 and 99 to get 27.72.

$$\frac{12}{-475+27.72}\left(-2\right)^{2}$$

Add -475 and 27.72 to get -447.28.

$$\frac{12}{-447.28}\left(-2\right)^{2}$$

Expand \frac{12}{-447.28} by multiplying both numerator and the denominator by 100.

$$\frac{1200}{-44728}\left(-2\right)^{2}$$

Reduce the fraction \frac{1200}{-44728} to lowest terms by extracting and canceling out 8.

$$-\frac{150}{5591}\left(-2\right)^{2}$$

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

$$-\frac{150}{5591}\times 4$$

Express -\frac{150}{5591}\times 4 as a single fraction.

$$\frac{-150\times 4}{5591}$$

Multiply -150 and 4 to get -600.

$$\frac{-600}{5591}$$

Fraction \frac{-600}{5591} can be rewritten as -\frac{600}{5591} by extracting the negative sign.

$$-\frac{600}{5591}$$

Factor

$$-\frac{600}{5591} = -0.10731532820604543$$