Solve -5^2*(-3^2/5)*2/9div(-1/2)^3div(-2)^2/5+20

$$- 5 ^ { 2 } \times ( - \frac { 3 ^ { 2 } } { 5 } ) \times \frac { 2 } { 9 } \div ( - \frac { 1 } { 2 } ) ^ { 3 } \div \frac { ( - 2 ) ^ { 2 } } { 5 } + 20$$

Evaluate

$$-80$$

Solution Steps

Divide \frac{\left(-5^{2}\right)\left(-\frac{3^{2}}{5}\right)\times \frac{2}{9}}{\left(-\frac{1}{2}\right)^{3}} by \frac{\left(-2\right)^{2}}{5} by multiplying \frac{\left(-5^{2}\right)\left(-\frac{3^{2}}{5}\right)\times \frac{2}{9}}{\left(-\frac{1}{2}\right)^{3}} by the reciprocal of \frac{\left(-2\right)^{2}}{5}.

$$\frac{\left(-5^{2}\right)\left(-\frac{3^{2}}{5}\right)\times \frac{2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-25\left(-\frac{3^{2}}{5}\right)\times \frac{2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Calculate 3 to the power of 2 and get 9.

$$\frac{-25\left(-\frac{9}{5}\right)\times \frac{2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Express -25\left(-\frac{9}{5}\right) as a single fraction.

$$\frac{\frac{-25\left(-9\right)}{5}\times \frac{2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Multiply -25 and -9 to get 225.

$$\frac{\frac{225}{5}\times \frac{2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Divide 225 by 5 to get 45.

$$\frac{45\times \frac{2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Express 45\times \frac{2}{9} as a single fraction.

$$\frac{\frac{45\times 2}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Multiply 45 and 2 to get 90.

$$\frac{\frac{90}{9}\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Divide 90 by 9 to get 10.

$$\frac{10\times 5}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Multiply 10 and 5 to get 50.

$$\frac{50}{\left(-\frac{1}{2}\right)^{3}\left(-2\right)^{2}}+20$$

Calculate -\frac{1}{2} to the power of 3 and get -\frac{1}{8}.

$$\frac{50}{-\frac{1}{8}\left(-2\right)^{2}}+20$$

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

$$\frac{50}{-\frac{1}{8}\times 4}+20$$

Express -\frac{1}{8}\times 4 as a single fraction.

$$\frac{50}{\frac{-4}{8}}+20$$

Reduce the fraction \frac{-4}{8} to lowest terms by extracting and canceling out 4.

$$\frac{50}{-\frac{1}{2}}+20$$

Divide 50 by -\frac{1}{2} by multiplying 50 by the reciprocal of -\frac{1}{2}.

$$50\left(-2\right)+20$$

Multiply 50 and -2 to get -100.

$$-100+20$$

Add -100 and 20 to get -80.

$$-80$$

Factor

$$-80$$