Solve (-5)*[(-1/85+18/17-1/5)*17-(-4/5)^2]-|-2*(-2)^3|

$$( - 5 ) \times [ ( - \frac { 1 } { 85 } + 1 \frac { 8 } { 17 } - \frac { 1 } { 5 } ) \times 17 - ( - \frac { 4 } { 5 } ) ^ { 2 } ] - | - 2 \times ( - 2 ) ^ { 3 } |$$

Evaluate

$$-\frac{599}{5}=-119.8$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$-5\left(\left(-\frac{1}{85}+\frac{17+8}{17}-\frac{1}{5}\right)\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Add 17 and 8 to get 25.

$$-5\left(\left(-\frac{1}{85}+\frac{25}{17}-\frac{1}{5}\right)\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Least common multiple of 85 and 17 is 85. Convert -\frac{1}{85} and \frac{25}{17} to fractions with denominator 85.

$$-5\left(\left(-\frac{1}{85}+\frac{125}{85}-\frac{1}{5}\right)\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Since -\frac{1}{85} and \frac{125}{85} have the same denominator, add them by adding their numerators.

$$-5\left(\left(\frac{-1+125}{85}-\frac{1}{5}\right)\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Add -1 and 125 to get 124.

$$-5\left(\left(\frac{124}{85}-\frac{1}{5}\right)\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Least common multiple of 85 and 5 is 85. Convert \frac{124}{85} and \frac{1}{5} to fractions with denominator 85.

$$-5\left(\left(\frac{124}{85}-\frac{17}{85}\right)\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Since \frac{124}{85} and \frac{17}{85} have the same denominator, subtract them by subtracting their numerators.

$$-5\left(\frac{124-17}{85}\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Subtract 17 from 124 to get 107.

$$-5\left(\frac{107}{85}\times 17-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Express \frac{107}{85}\times 17 as a single fraction.

$$-5\left(\frac{107\times 17}{85}-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Multiply 107 and 17 to get 1819.

$$-5\left(\frac{1819}{85}-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Reduce the fraction \frac{1819}{85} to lowest terms by extracting and canceling out 17.

$$-5\left(\frac{107}{5}-\left(-\frac{4}{5}\right)^{2}\right)-|\left(-2\right)^{4}|$$

Calculate -\frac{4}{5} to the power of 2 and get \frac{16}{25}.

$$-5\left(\frac{107}{5}-\frac{16}{25}\right)-|\left(-2\right)^{4}|$$

Least common multiple of 5 and 25 is 25. Convert \frac{107}{5} and \frac{16}{25} to fractions with denominator 25.

$$-5\left(\frac{535}{25}-\frac{16}{25}\right)-|\left(-2\right)^{4}|$$

Since \frac{535}{25} and \frac{16}{25} have the same denominator, subtract them by subtracting their numerators.

$$-5\times \frac{535-16}{25}-|\left(-2\right)^{4}|$$

Subtract 16 from 535 to get 519.

$$-5\times \frac{519}{25}-|\left(-2\right)^{4}|$$

Express -5\times \frac{519}{25} as a single fraction.

$$\frac{-5\times 519}{25}-|\left(-2\right)^{4}|$$

Multiply -5 and 519 to get -2595.

$$\frac{-2595}{25}-|\left(-2\right)^{4}|$$

Reduce the fraction \frac{-2595}{25} to lowest terms by extracting and canceling out 5.

$$-\frac{519}{5}-|\left(-2\right)^{4}|$$

Calculate -2 to the power of 4 and get 16.

$$-\frac{519}{5}-|16|$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of 16 is 16.

$$-\frac{519}{5}-16$$

Convert 16 to fraction \frac{80}{5}.

$$-\frac{519}{5}-\frac{80}{5}$$

Since -\frac{519}{5} and \frac{80}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-519-80}{5}$$

Subtract 80 from -519 to get -599.

$$-\frac{599}{5}$$

Factor

$$-\frac{599}{5} = -119\frac{4}{5} = -119.8$$