Solve (-41/20)*(-1.25)div(-1/2)^3div(-10)*(-1/3)^5*(-0.1^2)

$$( - 4 \frac { 1 } { 20 } ) \times ( - 1.25 ) \div ( - \frac { 1 } { 2 } ) ^ { 3 } \div ( - 10 ) \times ( - \frac { 1 } { 3 } ) ^ { 5 } \times ( - 0.1 ^ { 2 } )$$

Evaluate

$$\frac{1}{6000}\approx 0.000166667$$

Solution Steps

Express \frac{\frac{\left(-\frac{4\times 20+1}{20}\right)\left(-1.25\right)}{\left(-\frac{1}{2}\right)^{3}}}{-10} as a single fraction.

$$\frac{\left(-\frac{4\times 20+1}{20}\right)\left(-1.25\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Multiply 4 and 20 to get 80.

$$\frac{\left(-\frac{80+1}{20}\right)\left(-1.25\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Add 80 and 1 to get 81.

$$\frac{-\frac{81}{20}\left(-1.25\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Convert decimal number -1.25 to fraction -\frac{125}{100}. Reduce the fraction -\frac{125}{100} to lowest terms by extracting and canceling out 25.

$$\frac{-\frac{81}{20}\left(-\frac{5}{4}\right)}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Multiply -\frac{81}{20} times -\frac{5}{4} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-81\left(-5\right)}{20\times 4}}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Do the multiplications in the fraction \frac{-81\left(-5\right)}{20\times 4}.

$$\frac{\frac{405}{80}}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Reduce the fraction \frac{405}{80} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{81}{16}}{\left(-\frac{1}{2}\right)^{3}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

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

$$\frac{\frac{81}{16}}{-\frac{1}{8}\left(-10\right)}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

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

$$\frac{\frac{81}{16}}{\frac{-\left(-10\right)}{8}}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Multiply -1 and -10 to get 10.

$$\frac{\frac{81}{16}}{\frac{10}{8}}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

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

$$\frac{\frac{81}{16}}{\frac{5}{4}}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Divide \frac{81}{16} by \frac{5}{4} by multiplying \frac{81}{16} by the reciprocal of \frac{5}{4}.

$$\frac{81}{16}\times \frac{4}{5}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Multiply \frac{81}{16} times \frac{4}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 4}{16\times 5}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Do the multiplications in the fraction \frac{81\times 4}{16\times 5}.

$$\frac{324}{80}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

Reduce the fraction \frac{324}{80} to lowest terms by extracting and canceling out 4.

$$\frac{81}{20}\left(-\frac{1}{3}\right)^{5}\left(-0.1^{2}\right)$$

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

$$\frac{81}{20}\left(-\frac{1}{243}\right)\left(-0.1^{2}\right)$$

Multiply \frac{81}{20} times -\frac{1}{243} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\left(-1\right)}{20\times 243}\left(-0.1^{2}\right)$$

Do the multiplications in the fraction \frac{81\left(-1\right)}{20\times 243}.

$$\frac{-81}{4860}\left(-0.1^{2}\right)$$

Reduce the fraction \frac{-81}{4860} to lowest terms by extracting and canceling out 81.

$$-\frac{1}{60}\left(-0.1^{2}\right)$$

Calculate 0.1 to the power of 2 and get 0.01.

$$-\frac{1}{60}\left(-0.01\right)$$

Convert decimal number -0.01 to fraction -\frac{1}{100}.

$$-\frac{1}{60}\left(-\frac{1}{100}\right)$$

Multiply -\frac{1}{60} times -\frac{1}{100} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-\left(-1\right)}{60\times 100}$$

Do the multiplications in the fraction \frac{-\left(-1\right)}{60\times 100}.

$$\frac{1}{6000}$$

Factor

$$\frac{1}{3 \cdot 2 ^ {4} \cdot 5 ^ {3}} = 0.00016666666666666666$$