Solve (-41/20)*(-125)div(-1/2)^3div(-10)*(-1/3)^5*(-01^2)

$$( - 4 \frac { 1 } { 20 } ) \times ( - 125 ) \div ( - \frac { 1 } { 2 } ) ^ { 3 } \div ( - 10 ) \times ( - \frac { 1 } { 3 } ) ^ { 5 } \times ( - 01 ^ { 2 } )$$

Evaluate

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Solution Steps

Express \frac{\frac{\left(-\frac{4\times 20+1}{20}\right)\left(-125\right)}{\left(-\frac{1}{2}\right)^{3}}}{-10} as a single fraction.

$$\frac{\left(-\frac{4\times 20+1}{20}\right)\left(-125\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Multiply 4 and 20 to get 80.

$$\frac{\left(-\frac{80+1}{20}\right)\left(-125\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Add 80 and 1 to get 81.

$$\frac{-\frac{81}{20}\left(-125\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Express -\frac{81}{20}\left(-125\right) as a single fraction.

$$\frac{\frac{-81\left(-125\right)}{20}}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Multiply -81 and -125 to get 10125.

$$\frac{\frac{10125}{20}}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Reduce the fraction \frac{10125}{20} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{2025}{4}}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

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

$$\frac{\frac{2025}{4}}{-\frac{1}{8}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Express -\frac{1}{8}\left(-10\right) as a single fraction.

$$\frac{\frac{2025}{4}}{\frac{-\left(-10\right)}{8}}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Multiply -1 and -10 to get 10.

$$\frac{\frac{2025}{4}}{\frac{10}{8}}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Reduce the fraction \frac{10}{8} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{2025}{4}}{\frac{5}{4}}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Divide \frac{2025}{4} by \frac{5}{4} by multiplying \frac{2025}{4} by the reciprocal of \frac{5}{4}.

$$\frac{2025}{4}\times \frac{4}{5}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Multiply \frac{2025}{4} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2025\times 4}{4\times 5}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Cancel out 4 in both numerator and denominator.

$$\frac{2025}{5}\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Divide 2025 by 5 to get 405.

$$405\left(-\frac{1}{3}\right)^{5}\times 0\times 1^{2}$$

Calculate -\frac{1}{3} to the power of 5 and get -\frac{1}{243}.

$$405\left(-\frac{1}{243}\right)\times 0\times 1^{2}$$

Express 405\left(-\frac{1}{243}\right) as a single fraction.

$$\frac{405\left(-1\right)}{243}\times 0\times 1^{2}$$

Multiply 405 and -1 to get -405.

$$\frac{-405}{243}\times 0\times 1^{2}$$

Reduce the fraction \frac{-405}{243} to lowest terms by extracting and canceling out 81.

$$-\frac{5}{3}\times 0\times 1^{2}$$

Multiply -\frac{5}{3} and 0 to get 0.

$$0\times 1^{2}$$

Calculate 1 to the power of 2 and get 1.

$$0\times 1$$

Multiply 0 and 1 to get 0.

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Factor

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