Solve 1-41-2^-2+2020^circ-2*8^-2div2^-2

$$1 - 41 - 2 ^ { - 2 } + 2020 ^ { \circ } - 2 \times 8 ^ { - 2 } \div 2 ^ { - 2 }$$

Evaluate

$$\frac{15837}{8}=1979.625$$

Solution Steps

Subtract 41 from 1 to get -40.

$$-40-2^{-2}+2020-\frac{2\times 8^{-2}}{2^{-2}}$$

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

$$-40-\frac{1}{4}+2020-\frac{2\times 8^{-2}}{2^{-2}}$$

Subtract \frac{1}{4} from -40 to get -\frac{161}{4}.

$$-\frac{161}{4}+2020-\frac{2\times 8^{-2}}{2^{-2}}$$

Add -\frac{161}{4} and 2020 to get \frac{7919}{4}.

$$\frac{7919}{4}-\frac{2\times 8^{-2}}{2^{-2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{7919}{4}-2^{3}\times 8^{-2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{7919}{4}-8\times 8^{-2}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{7919}{4}-8\times \frac{1}{64}$$

Multiply 8 and \frac{1}{64} to get \frac{1}{8}.

$$\frac{7919}{4}-\frac{1}{8}$$

Subtract \frac{1}{8} from \frac{7919}{4} to get \frac{15837}{8}.

$$\frac{15837}{8}$$

Factor

$$\frac{3 \cdot 5279}{2 ^ {3}} = 1979\frac{5}{8} = 1979.625$$