Solve 10*(1/6)^2*(5/6)^3

$$10 \cdot ( \frac { 1 } { 6 } ) ^ { 2 } \cdot ( \frac { 5 } { 6 } ) ^ { 3 }$$

Evaluate

$$\frac{625}{3888}\approx 0.160751029$$

Solution Steps

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$10\times \frac{1}{36}\times \left(\frac{5}{6}\right)^{3}$$

Multiply 10 and \frac{1}{36} to get \frac{10}{36}.

$$\frac{10}{36}\times \left(\frac{5}{6}\right)^{3}$$

Reduce the fraction \frac{10}{36} to lowest terms by extracting and canceling out 2.

$$\frac{5}{18}\times \left(\frac{5}{6}\right)^{3}$$

Calculate \frac{5}{6} to the power of 3 and get \frac{125}{216}.

$$\frac{5}{18}\times \frac{125}{216}$$

Multiply \frac{5}{18} times \frac{125}{216} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5\times 125}{18\times 216}$$

Do the multiplications in the fraction \frac{5\times 125}{18\times 216}.

$$\frac{625}{3888}$$

Factor

$$\frac{5 ^ {4}}{2 ^ {4} \cdot 3 ^ {5}} = 0.16075102880658437$$