Solve |-4|-2^-2+2020^0-2*8^-2div2^-2

$$| - 4 | - 2 ^ { - 2 } + 2020 ^ { 0 } - 2 \times 8 ^ { - 2 } \div 2 ^ { - 2 }$$

Evaluate

$$\frac{37}{8}=4.625$$

Solution Steps

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -4 is 4.

$$4-2^{-2}+2020^{0}-\frac{2\times 8^{-2}}{2^{-2}}$$

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

$$4-\frac{1}{4}+2020^{0}-\frac{2\times 8^{-2}}{2^{-2}}$$

Subtract \frac{1}{4} from 4 to get \frac{15}{4}.

$$\frac{15}{4}+2020^{0}-\frac{2\times 8^{-2}}{2^{-2}}$$

Calculate 2020 to the power of 0 and get 1.

$$\frac{15}{4}+1-\frac{2\times 8^{-2}}{2^{-2}}$$

Add \frac{15}{4} and 1 to get \frac{19}{4}.

$$\frac{19}{4}-\frac{2\times 8^{-2}}{2^{-2}}$$

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

$$\frac{19}{4}-2^{3}\times 8^{-2}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{19}{4}-8\times 8^{-2}$$

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

$$\frac{19}{4}-8\times \frac{1}{64}$$

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

$$\frac{19}{4}-\frac{1}{8}$$

Subtract \frac{1}{8} from \frac{19}{4} to get \frac{37}{8}.

$$\frac{37}{8}$$

Factor

$$\frac{37}{2 ^ {3}} = 4\frac{5}{8} = 4.625$$