Solve 8/4(82-2)-2(3^3-2^7/5)

$$\frac { 8 } { 4 } ( 82 - 2 ) - 2 ( \frac { 3 ^ { 3 } - 2 ^ { 7 } } { 5 } )$$

Evaluate

$$\frac{1002}{5}=200.4$$

Solution Steps

Divide 8 by 4 to get 2.

$$2\left(82-2\right)-2\times \frac{3^{3}-2^{7}}{5}$$

Subtract 2 from 82 to get 80.

$$2\times 80-2\times \frac{3^{3}-2^{7}}{5}$$

Multiply 2 and 80 to get 160.

$$160-2\times \frac{3^{3}-2^{7}}{5}$$

Calculate 3 to the power of 3 and get 27.

$$160-2\times \frac{27-2^{7}}{5}$$

Calculate 2 to the power of 7 and get 128.

$$160-2\times \frac{27-128}{5}$$

Subtract 128 from 27 to get -101.

$$160-2\times \frac{-101}{5}$$

Fraction \frac{-101}{5} can be rewritten as -\frac{101}{5} by extracting the negative sign.

$$160-2\left(-\frac{101}{5}\right)$$

Express 2\left(-\frac{101}{5}\right) as a single fraction.

$$160-\frac{2\left(-101\right)}{5}$$

Multiply 2 and -101 to get -202.

$$160-\frac{-202}{5}$$

Fraction \frac{-202}{5} can be rewritten as -\frac{202}{5} by extracting the negative sign.

$$160-\left(-\frac{202}{5}\right)$$

The opposite of -\frac{202}{5} is \frac{202}{5}.

$$160+\frac{202}{5}$$

Convert 160 to fraction \frac{800}{5}.

$$\frac{800}{5}+\frac{202}{5}$$

Since \frac{800}{5} and \frac{202}{5} have the same denominator, add them by adding their numerators.

$$\frac{800+202}{5}$$

Add 800 and 202 to get 1002.

$$\frac{1002}{5}$$

Factor

$$\frac{2 \cdot 3 \cdot 167}{5} = 200\frac{2}{5} = 200.4$$