Solve (27/125)^1/3*[(3/2)^-2div(2/5)^3]-4(3/7)^0

$$( \frac { 27 } { 125 } ) ^ { 1 / 3 } \times [ ( \frac { 3 } { 2 } ) ^ { - 2 } \div ( \frac { 2 } { 5 } ) ^ { 3 } ] - 4 ( \frac { 3 } { 7 } ) ^ { 0 }$$

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

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

$$\frac{3}{5}\times \frac{\left(\frac{3}{2}\right)^{-2}}{\left(\frac{2}{5}\right)^{3}}-4\times \left(\frac{3}{7}\right)^{0}$$

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

$$\frac{3}{5}\times \frac{\frac{4}{9}}{\left(\frac{2}{5}\right)^{3}}-4\times \left(\frac{3}{7}\right)^{0}$$

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

$$\frac{3}{5}\times \frac{\frac{4}{9}}{\frac{8}{125}}-4\times \left(\frac{3}{7}\right)^{0}$$

Divide \frac{4}{9} by \frac{8}{125} by multiplying \frac{4}{9} by the reciprocal of \frac{8}{125}.

$$\frac{3}{5}\times \frac{4}{9}\times \frac{125}{8}-4\times \left(\frac{3}{7}\right)^{0}$$

Multiply \frac{4}{9} and \frac{125}{8} to get \frac{125}{18}.

$$\frac{3}{5}\times \frac{125}{18}-4\times \left(\frac{3}{7}\right)^{0}$$

Multiply \frac{3}{5} and \frac{125}{18} to get \frac{25}{6}.

$$\frac{25}{6}-4\times \left(\frac{3}{7}\right)^{0}$$

Calculate \frac{3}{7} to the power of 0 and get 1.

$$\frac{25}{6}-4\times 1$$

Multiply 4 and 1 to get 4.

$$\frac{25}{6}-4$$

Subtract 4 from \frac{25}{6} to get \frac{1}{6}.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$