Solve (3/2^{2})^{-1}:4/3-(2^-1/3^-2+1)*3/-4-frac{2^-3}{(-1)^2021}

$$( \frac { 3 } { 2 ^ { 2 } } ) ^ { - 1 } : \frac { 4 } { 3 } - ( \frac { 2 ^ { - 1 } } { 3 ^ { - 2 } } + 1 ) \cdot \frac { 3 } { - 4 } - \frac { 2 ^ { - 3 } } { ( - 1 ) ^ { 2021 } }$$

Evaluate

$$\frac{21}{4}=5.25$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(\frac{3}{4}\right)^{-1}}{\frac{4}{3}}-\left(\frac{2^{-1}}{3^{-2}}+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Calculate \frac{3}{4} to the power of -1 and get \frac{4}{3}.

$$\frac{\frac{4}{3}}{\frac{4}{3}}-\left(\frac{2^{-1}}{3^{-2}}+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Divide \frac{4}{3} by \frac{4}{3} to get 1.

$$1-\left(\frac{2^{-1}}{3^{-2}}+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

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

$$1-\left(\frac{\frac{1}{2}}{3^{-2}}+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$1-\left(\frac{\frac{1}{2}}{\frac{1}{9}}+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Divide \frac{1}{2} by \frac{1}{9} by multiplying \frac{1}{2} by the reciprocal of \frac{1}{9}.

$$1-\left(\frac{1}{2}\times 9+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Multiply \frac{1}{2} and 9 to get \frac{9}{2}.

$$1-\left(\frac{9}{2}+1\right)\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Add \frac{9}{2} and 1 to get \frac{11}{2}.

$$1-\frac{11}{2}\times \frac{3}{-4}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Fraction \frac{3}{-4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$1-\frac{11}{2}\left(-\frac{3}{4}\right)-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Multiply \frac{11}{2} and -\frac{3}{4} to get -\frac{33}{8}.

$$1-\left(-\frac{33}{8}\right)-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

The opposite of -\frac{33}{8} is \frac{33}{8}.

$$1+\frac{33}{8}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Add 1 and \frac{33}{8} to get \frac{41}{8}.

$$\frac{41}{8}-\frac{2^{-3}}{\left(-1\right)^{2021}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{41}{8}-\frac{\frac{1}{8}}{\left(-1\right)^{2021}}$$

Calculate -1 to the power of 2021 and get -1.

$$\frac{41}{8}-\frac{\frac{1}{8}}{-1}$$

Express \frac{\frac{1}{8}}{-1} as a single fraction.

$$\frac{41}{8}-\frac{1}{8\left(-1\right)}$$

Multiply 8 and -1 to get -8.

$$\frac{41}{8}-\frac{1}{-8}$$

Fraction \frac{1}{-8} can be rewritten as -\frac{1}{8} by extracting the negative sign.

$$\frac{41}{8}-\left(-\frac{1}{8}\right)$$

The opposite of -\frac{1}{8} is \frac{1}{8}.

$$\frac{41}{8}+\frac{1}{8}$$

Add \frac{41}{8} and \frac{1}{8} to get \frac{21}{4}.

$$\frac{21}{4}$$

Factor

$$\frac{3 \cdot 7}{2 ^ {2}} = 5\frac{1}{4} = 5.25$$