Solve [(5/2)^3div(3/2)^4]*(3/5)^3

$$[ ( \frac { 5 } { 2 } ) ^ { 3 } \div ( \frac { 3 } { 2 } ) ^ { 4 } ] \times ( \frac { 3 } { 5 } ) ^ { 3 }$$

Evaluate

$$\frac{2}{3}\approx 0.666666667$$

Solution Steps

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

$$\frac{\frac{125}{8}}{\left(\frac{3}{2}\right)^{4}}\times \left(\frac{3}{5}\right)^{3}$$

Calculate \frac{3}{2} to the power of 4 and get \frac{81}{16}.

$$\frac{\frac{125}{8}}{\frac{81}{16}}\times \left(\frac{3}{5}\right)^{3}$$

Divide \frac{125}{8} by \frac{81}{16} by multiplying \frac{125}{8} by the reciprocal of \frac{81}{16}.

$$\frac{125}{8}\times \frac{16}{81}\times \left(\frac{3}{5}\right)^{3}$$

Multiply \frac{125}{8} times \frac{16}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{125\times 16}{8\times 81}\times \left(\frac{3}{5}\right)^{3}$$

Do the multiplications in the fraction \frac{125\times 16}{8\times 81}.

$$\frac{2000}{648}\times \left(\frac{3}{5}\right)^{3}$$

Reduce the fraction \frac{2000}{648} to lowest terms by extracting and canceling out 8.

$$\frac{250}{81}\times \left(\frac{3}{5}\right)^{3}$$

Calculate \frac{3}{5} to the power of 3 and get \frac{27}{125}.

$$\frac{250}{81}\times \frac{27}{125}$$

Multiply \frac{250}{81} times \frac{27}{125} by multiplying numerator times numerator and denominator times denominator.

$$\frac{250\times 27}{81\times 125}$$

Do the multiplications in the fraction \frac{250\times 27}{81\times 125}.

$$\frac{6750}{10125}$$

Reduce the fraction \frac{6750}{10125} to lowest terms by extracting and canceling out 3375.

$$\frac{2}{3}$$

Factor

$$\frac{2}{3} = 0.6666666666666666$$