Solve (56/28)div(2/5)^3*16/25

$$( \frac { 56 } { 28 } ) \div ( \frac { 2 } { 5 } ) ^ { 3 } \times \frac { 16 } { 25 }$$

Evaluate

$$20$$

Solution Steps

Divide 56 by 28 to get 2.

$$\frac{2}{\left(\frac{2}{5}\right)^{3}}\times \frac{16}{25}$$

Calculate \frac{2}{5} to the power of 3 and get \frac{8}{125}.

$$\frac{2}{\frac{8}{125}}\times \frac{16}{25}$$

Divide 2 by \frac{8}{125} by multiplying 2 by the reciprocal of \frac{8}{125}.

$$2\times \frac{125}{8}\times \frac{16}{25}$$

Express 2\times \frac{125}{8} as a single fraction.

$$\frac{2\times 125}{8}\times \frac{16}{25}$$

Multiply 2 and 125 to get 250.

$$\frac{250}{8}\times \frac{16}{25}$$

Reduce the fraction \frac{250}{8} to lowest terms by extracting and canceling out 2.

$$\frac{125}{4}\times \frac{16}{25}$$

Multiply \frac{125}{4} times \frac{16}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125\times 16}{4\times 25}$$

Do the multiplications in the fraction \frac{125\times 16}{4\times 25}.

$$\frac{2000}{100}$$

Divide 2000 by 100 to get 20.

$$20$$

Factor

$$2^{2}\times 5$$