Solve (56/28)div(2/5)^3*16/25/1div(2)^3*16

$$\frac { ( \frac { 56 } { 28 } ) \div ( \frac { 2 } { 5 } ) ^ { 3 } \times \frac { 16 } { 25 } } { 1 \div ( 2 ) ^ { 3 } \times 16 }$$

Evaluate

$$10$$

Solution Steps

Divide 56 by 28 to get 2.

$$\frac{\frac{2}{\left(\frac{2}{5}\right)^{3}}\times \frac{16}{25}}{\frac{1}{2^{3}}\times 16}$$

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

$$\frac{\frac{2}{\frac{8}{125}}\times \frac{16}{25}}{\frac{1}{2^{3}}\times 16}$$

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

$$\frac{2\times \frac{125}{8}\times \frac{16}{25}}{\frac{1}{2^{3}}\times 16}$$

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

$$\frac{\frac{2\times 125}{8}\times \frac{16}{25}}{\frac{1}{2^{3}}\times 16}$$

Multiply 2 and 125 to get 250.

$$\frac{\frac{250}{8}\times \frac{16}{25}}{\frac{1}{2^{3}}\times 16}$$

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

$$\frac{\frac{125}{4}\times \frac{16}{25}}{\frac{1}{2^{3}}\times 16}$$

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

$$\frac{\frac{125\times 16}{4\times 25}}{\frac{1}{2^{3}}\times 16}$$

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

$$\frac{\frac{2000}{100}}{\frac{1}{2^{3}}\times 16}$$

Divide 2000 by 100 to get 20.

$$\frac{20}{\frac{1}{2^{3}}\times 16}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{20}{\frac{1}{8}\times 16}$$

Multiply \frac{1}{8} and 16 to get \frac{16}{8}.

$$\frac{20}{\frac{16}{8}}$$

Divide 16 by 8 to get 2.

$$\frac{20}{2}$$

Divide 20 by 2 to get 10.

$$10$$

Factor

$$2\times 5$$