Solve (27/125)^1/3*[(3/2)^-2div1(2/5)^3]-4(3/7)^2

$$( \frac { 27 } { 125 } ) ^ { 1 / 3 } \times [ ( \frac { 3 } { 2 } ) ^ { - 2 } \div 1 ( \frac { 2 } { 5 } ) ^ { 3 } ] - 4 ( \frac { 3 } { 7 } ) ^ { 2 }$$

Evaluate

$$-\frac{65932}{91875}\approx -0.717627211$$

Solution Steps

Calculate \frac{27}{125} to the power of \frac{1}{3} and get \frac{3}{5}.

$$\frac{3}{5}\times \frac{\left(\frac{3}{2}\right)^{-2}}{1}\times \left(\frac{2}{5}\right)^{3}-4\times \left(\frac{3}{7}\right)^{2}$$

Calculate \frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$\frac{3}{5}\times \frac{\frac{4}{9}}{1}\times \left(\frac{2}{5}\right)^{3}-4\times \left(\frac{3}{7}\right)^{2}$$

Anything divided by one gives itself.

$$\frac{3}{5}\times \frac{4}{9}\times \left(\frac{2}{5}\right)^{3}-4\times \left(\frac{3}{7}\right)^{2}$$

Multiply \frac{3}{5} and \frac{4}{9} to get \frac{4}{15}.

$$\frac{4}{15}\times \left(\frac{2}{5}\right)^{3}-4\times \left(\frac{3}{7}\right)^{2}$$

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

$$\frac{4}{15}\times \frac{8}{125}-4\times \left(\frac{3}{7}\right)^{2}$$

Multiply \frac{4}{15} and \frac{8}{125} to get \frac{32}{1875}.

$$\frac{32}{1875}-4\times \left(\frac{3}{7}\right)^{2}$$

Calculate \frac{3}{7} to the power of 2 and get \frac{9}{49}.

$$\frac{32}{1875}-4\times \frac{9}{49}$$

Multiply 4 and \frac{9}{49} to get \frac{36}{49}.

$$\frac{32}{1875}-\frac{36}{49}$$

Subtract \frac{36}{49} from \frac{32}{1875} to get -\frac{65932}{91875}.

$$-\frac{65932}{91875}$$

Factor

$$-\frac{65932}{91875} = -0.7176272108843538$$