Solve -5/4+5/2*[(-3/5)^2-(1/2)^4*(-32)]div(-2frac{4}{5})

$$- \frac { 5 } { 4 } + \frac { 5 } { 2 } \times [ ( - \frac { 3 } { 5 } ) ^ { 2 } - ( \frac { 1 } { 2 } ) ^ { 4 } \times ( - 32 ) ] \div ( - 2 \frac { 4 } { 5 } )$$

Evaluate

$$-\frac{47}{14}\approx -3.357142857$$

Solution Steps

Calculate -\frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\left(\frac{1}{2}\right)^{4}\left(-32\right)\right)}{-\frac{2\times 5+4}{5}}$$

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{1}{16}\left(-32\right)\right)}{-\frac{2\times 5+4}{5}}$$

Multiply \frac{1}{16} and -32 to get \frac{-32}{16}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\frac{-32}{16}\right)}{-\frac{2\times 5+4}{5}}$$

Divide -32 by 16 to get -2.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}-\left(-2\right)\right)}{-\frac{2\times 5+4}{5}}$$

The opposite of -2 is 2.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}+2\right)}{-\frac{2\times 5+4}{5}}$$

Convert 2 to fraction \frac{50}{25}.

$$-\frac{5}{4}+\frac{\frac{5}{2}\left(\frac{9}{25}+\frac{50}{25}\right)}{-\frac{2\times 5+4}{5}}$$

Since \frac{9}{25} and \frac{50}{25} have the same denominator, add them by adding their numerators.

$$-\frac{5}{4}+\frac{\frac{5}{2}\times \frac{9+50}{25}}{-\frac{2\times 5+4}{5}}$$

Add 9 and 50 to get 59.

$$-\frac{5}{4}+\frac{\frac{5}{2}\times \frac{59}{25}}{-\frac{2\times 5+4}{5}}$$

Multiply \frac{5}{2} times \frac{59}{25} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{4}+\frac{\frac{5\times 59}{2\times 25}}{-\frac{2\times 5+4}{5}}$$

Do the multiplications in the fraction \frac{5\times 59}{2\times 25}.

$$-\frac{5}{4}+\frac{\frac{295}{50}}{-\frac{2\times 5+4}{5}}$$

Reduce the fraction \frac{295}{50} to lowest terms by extracting and canceling out 5.

$$-\frac{5}{4}+\frac{\frac{59}{10}}{-\frac{2\times 5+4}{5}}$$

Multiply 2 and 5 to get 10.

$$-\frac{5}{4}+\frac{\frac{59}{10}}{-\frac{10+4}{5}}$$

Add 10 and 4 to get 14.

$$-\frac{5}{4}+\frac{\frac{59}{10}}{-\frac{14}{5}}$$

Divide \frac{59}{10} by -\frac{14}{5} by multiplying \frac{59}{10} by the reciprocal of -\frac{14}{5}.

$$-\frac{5}{4}+\frac{59}{10}\left(-\frac{5}{14}\right)$$

Multiply \frac{59}{10} times -\frac{5}{14} by multiplying numerator times numerator and denominator times denominator.

$$-\frac{5}{4}+\frac{59\left(-5\right)}{10\times 14}$$

Do the multiplications in the fraction \frac{59\left(-5\right)}{10\times 14}.

$$-\frac{5}{4}+\frac{-295}{140}$$

Reduce the fraction \frac{-295}{140} to lowest terms by extracting and canceling out 5.

$$-\frac{5}{4}-\frac{59}{28}$$

Least common multiple of 4 and 28 is 28. Convert -\frac{5}{4} and \frac{59}{28} to fractions with denominator 28.

$$-\frac{35}{28}-\frac{59}{28}$$

Since -\frac{35}{28} and \frac{59}{28} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-35-59}{28}$$

Subtract 59 from -35 to get -94.

$$\frac{-94}{28}$$

Reduce the fraction \frac{-94}{28} to lowest terms by extracting and canceling out 2.

$$-\frac{47}{14}$$

Factor

$$-\frac{47}{14} = -3\frac{5}{14} = -3.357142857142857$$