Solve [1/5*1/6*2/9:1/16]^3:frac{1}{8}

$$[ \frac { 1 } { 5 } \cdot \frac { 1 } { 6 } \cdot \frac { 2 } { 9 } : \frac { 1 } { 16 } ] ^ { 3 } : \frac { 1 } { 8 }$$

Evaluate

$$\frac{32768}{2460375}\approx 0.013318295$$

Solution Steps

Multiply \frac{1}{5} and \frac{1}{6} to get \frac{1}{30}.

$$\frac{\left(\frac{\frac{1}{30}\times \frac{2}{9}}{\frac{1}{16}}\right)^{3}}{\frac{1}{8}}$$

Multiply \frac{1}{30} and \frac{2}{9} to get \frac{1}{135}.

$$\frac{\left(\frac{\frac{1}{135}}{\frac{1}{16}}\right)^{3}}{\frac{1}{8}}$$

Divide \frac{1}{135} by \frac{1}{16} by multiplying \frac{1}{135} by the reciprocal of \frac{1}{16}.

$$\frac{\left(\frac{1}{135}\times 16\right)^{3}}{\frac{1}{8}}$$

Multiply \frac{1}{135} and 16 to get \frac{16}{135}.

$$\frac{\left(\frac{16}{135}\right)^{3}}{\frac{1}{8}}$$

Calculate \frac{16}{135} to the power of 3 and get \frac{4096}{2460375}.

$$\frac{\frac{4096}{2460375}}{\frac{1}{8}}$$

Divide \frac{4096}{2460375} by \frac{1}{8} by multiplying \frac{4096}{2460375} by the reciprocal of \frac{1}{8}.

$$\frac{4096}{2460375}\times 8$$

Multiply \frac{4096}{2460375} and 8 to get \frac{32768}{2460375}.

$$\frac{32768}{2460375}$$

Factor

$$\frac{2 ^ {15}}{3 ^ {9} \cdot 5 ^ {3}} = 0.013318294975359447$$